CFA TI BA II Plus Professional User manual

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 1
CFALA REVIEW MATERIALS
USING THE TI-BAII PLUS
CALCULATOR
David Cary, PhD, CFA
Spring 2015
[e-mail]
(helpful if you put CFA Review in subject line)
UsingtheTI‐BA2+
NotesbyDavidCary
Theseshouldhelpyoubemoreefficientwith
yourcalculator.
ForsomeofthetopicsIshowmorethanone
waytodoacalculation.
SomeoftheseslidesareintheLevelIlecture
notesandothersarenew.
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CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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TI BA II Plus
Professional
(there is a newer
version that looks
different)
TI BA II
Plus
CFA Exam acceptable calculators
Have a fresh battery,
Consider taking a spare
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BASIC SETUP
• To set the number of decimal places:
4
Keys Display Comments
[2nd][FORMAT] DEC = 2.00 Current setting
4 [ENTER] DEC= 4.0000 New setting
6 [ENTER] DEC= 6.000000 New setting, etc.
CE/C 6.000000 Ready to go
To clear memories
Deletes last digit entered
[CE/C] Sets display value to 0
[2nd] [CLR TVM] (above FV key) Sets N, I, PV, PMT, FV to 0.0
[2nd] [DATA] [2nd] [CLR WORK] Clears Statistical memories
[CF] [2nd] [CLR WORK] Clears Cash Flow memories
I usually set
for 4 places
then change
if necessary.

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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ORDER OF OPERATIONS
• In the rules of algebra, calculations should be done in the following
order:
Items in parentheses, exponents and roots, multiplication and
division, and finally addition and subtraction.
For items in equal levels, go from left to right.
For example, the correct order for “2 3 + 4 5” should be 2 3 = 6,
“4 5 = 20” and then “6 + 20” = 26.
BUT, the default method in your calculator will probably chain the
calculations in left to right order and do “2 3 = 6”, “6 + 4 = 10”, “10 5
= 50”. Not the right answer.
There are three methods discussed below to get the correct answer,
relatively efficiently, with examples:
1. Using your calculator memories,
2. Using parentheses, and
3. Switching the TI-BAII+ into “AOS” “Algebraic Operating System.”
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USING CHN OR AOS
The default setting in your calculator is probably “Chn” which stands for chaining.
Calculations are done in the order they are entered.
• Using the previous example: If the equation is 2x3 + 4x5 and the values and
operators are entered in that order the results will be 2x3 = 6, 6+4 = 10, 10x5 =
50. To get the correct answer, either the calculator memories need to be used
or parentheses (steps shown in following slides).
The alternative setting is AOS, Algebraic Operating System. It follows the rule of
order for algebra.
• For the same example it would do the following:
When you enter the ‘+’ sign after 2x3 it multiplies the 2x3 to get 6 as
multiplication has priority over addition.
It holds the “6+” in memory to see what is next.
When the 4 is entered it doesn’t do anything yet.
Then when the “x 5 =“ is entered it knows it should multiply “4x5” and then add
“6” to get the correct answer of “26”. 6

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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USING CHN OR AOS
• To get to AOS, use [2nd] [FORMAT] and the screen will show the decimal
setting.
• Use up arrow and it will say Chn orAOS.
• If it says Chn, use [2nd] [SET] to change to AOS.
• If it says AOS, it is ready to go.
• You can use [2nd] [SET] again to change back to Chn.
• Then hit [CE/C] to start.
•(You can switch back and forth if you wish, I stay with AOS)
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USING MEMORIES
• Your calculator has 10 easily accessible memories: #0 to #9.
• You can store numbers in a memory by pressing [STO] [n]
where [n] in the number of the memory where you want to store
the number.
For example: 3 [STO] [1] will store the number 3 in memory #1.
• You can recall a stored number by pressing [RCL] [n] where [n]
is the number of the memory you want to recall. For example:
[RCL] [1] will give the value 3 (assuming you stored it in the
previous step above).
• You do not need to clear memories because when you store a
number it over-writes any value that may have been there
before. 8

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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ADDING, SUBTRACTING, MULTIPLYING AND
DIVIDING TO MEMORIES!
• The following steps can also be done with memories, but be
careful, one missed step messes up the numbers.
3 [STO][1] puts 3 in Memory #1
(assume each step below is done in sequence).
Then if you press 4 [STO] [+] 1, the value in #1 will be 7.00, (3+4=7)
Then if you press 4 [STO] [] 1, the value in #1 will be 3.00, (7 4=3)
Then if you press 4 [STO] [x] 1, the value in #1 will be 12.00,
(3x4=12) and
Then if you press 4 [STO][] 1, the value in #1 will be 3.00 (12 4=3).
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CALCULATING MEANS AND COVARIANCES OF
TWO ASSET PORTFOLIO
• Example from D.Cary’s Level I CFALA review
lecture notes, SS 2, Reading 8:
• The question is to find the expected return “rp” and
the variance (and standard deviation) of this portfolio.
• Before doing the calculations, look at the numbers carefully.
A weight of 75% will be entered as 0.75
A return of 20% can be entered as 20 and the answer will be in “%” value or
as 0.20 and the answer will be in decimal value “0.00”.
Note if they give you Variance or Standard Deviation. For part of the
equations used you might need variance and other parts might need
standard deviation.
Also note if they give you the covariance or correlation of the two assets.
Remember that covariance = correlation x s1x s2.
The following pages use “s12” to denote covariance. 10
12
w 75% 25%
r 20% 12%
var 625 196
Covar 120

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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1. USING MEMORIES (Chn or AOS):
•r
p= r1w1+ r2w2
1: 0.75 20 = 15 [STO] [1] “stores first step in #1”
2: 0.25 12 = 3 [STO] [2] “stores second step in #2”
3: [RCL] [1] + [RCL][2] = 18 “adds #1 and #2 to get answer”
•s
p2= w12s12+ w22s22+ 2 w1w2s12
1: 0.75[x2] 625 = 351.56 [STO][1]
2: 0.25[x2] 196 = 12.25 [STO][2]
3: 2 0.75 0.25 120 = 45.00[STO] [3]
4: [RCL] [1] + [RCL][2] + [RCL][3] = 408.81 “the variance”
5: [ x] = 20.22% “the standard deviation is 20.22%”
• Remember if they give you the standard deviations, you have to square them
to get the variance for the first two parts of the equation just like you squared
the weights. If they give you correlation you have to multiply by the standard
deviations to get covariance for the third part.
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CALCULATING MEANS AND COVARIANCES OF
TWO ASSET PORTFOLIO
12
w 75% 25%
r 20% 12%
var 625 196
Covar 120
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2. USING PARENTHESES (Chn or AOS):
•r
p= r1w1+ r2w2
1: 0.75 20 + (0.25 12) = 18
“the parentheses are above the numbers 7 & 8”
“they are NOT needed for the first calculation since it is multiplication”
“you do not really need the last parenthesis, the ‘= will be enough”
•s
p2= w12s12+ w22s22+ 2 w1w2s12
1: 0.75[x2] 625 + (0.25[x2] 196) + (2 0.75 0.25 120) = 408.81
“the variance”
5: [ x] = 20.22% “the standard deviation”
• Even though the parentheses method works fine, I would consider
using the memory method on the previous slide to avoid errors for
longer calculations, such as for the variance.
• See previous bottom note if given standard deviations and/or correlations.
CALCULATING MEANS AND COVARIANCES OF
TWO ASSET PORTFOLIO
12
w 75% 25%
r 20% 12%
var 625 196
Covar 120

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 7
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13
3. USING AOS (NOT Chn):
To get to AOS, use [2nd] [FORMAT] and the screen
will show the decimal setting.
Use up arrow and it may say Chn or AOS. If it says
Chn, use [2nd] [SET] to change toAOS. If it says AOS, it is ready to go.
Then hit [CE/C] to start. (You can switch back and forth, I use AOS)
•r
p= r1w1+ r2w2
1: 0.75 20 + 0.25 12 = 18
“no parenthesis or memories needed for calculation!”
•s
p2= w12s12+ w22s22+ 2 w1w2s12
1: 0.75[x2] 625 + 0.25[x2] 196 + 2 0.75 0.25 120 = 408.81
“the variance”
5: [ x] = 20.22 “the standard deviation si 20.22%”
• See previous bottom note if given standard deviations and/or correlations.
13
CALCULATING MEANS AND COVARIANCES OF
TWO ASSET PORTFOLIO
12
w 75% 25%
r 20% 12%
var 625 196
Covar 120
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WHICH METHOD TO USE
• I like AOS. For the simpler calculations you can do them directly. For
more complicated calculations you can still use the memory or
parenthesis methods even if the calculator is in AOS mode.
• For example, I would probably do the “rp” calculation on the previous
page usingAOS, nice and simple. But for the sp2calculation, I might
use the memory method so if I messed up a calculation towards the
end of the equation, I wouldn’t have to start all over.
• If you want to use AOS mode, please check on a regular basis it is still
in AOS mode. An accidental reset may change it back to Chn.
• Not sure why you would want to but you can easily change back and
forth betweenAOS and Chn by using the [2nd] [FORMAT], then up
arrow, then [2nd][SET]. 14

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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Enter Shows Explanation
[2nd] [BEG] END Shows current setting
[2nd] [SET] BEG Shows new setting
[CE/C] BEG
0.0000 Should show BEG above number
To Reset after calculation…
[2nd] [BEG] BEG Shows current setting
[2nd] [SET] END Shows new setting
[CE/C] 0.0000 Blank above number
This is for Annuities Due where the payment is at the
beginning of each period:
Note: The [BEG] key is above the [PMT] key.
Calculator Hints – BEG mode
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Calculator Hints: # of Pmts/Yr
While I prefer to adjust N and I directly, the TI can be set
to do the calculations (for daily or …):
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Enter Shows Explanation
[2nd] [I/Y] P/Y = 1.0000 Shows current setting
365[ENTER] P/Y = 365.0000 Shows new setting
[CE/C] 365.0000 P/Y set
To Reset after calculation…
[2nd] [I/Y] P/Y = 365.0000 Shows current setting
1[ENTER] P/Y = 1.0000 Shows new setting
[CE/C] 1.0000 P/Y set
When you use P/Y, enter N = (P/Y) (# of years), I = I.
I would recommend getting into the habit of checking
the P/Y setting before doing TVM problems

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 9
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Uneven cash flows
• To find the PV (or FV) of uneven cash flows,
find the PV (or FV) of each cash flow and add
them together.
• Learn how to use ‘CF’ keys on your calculator
or use the ‘table method’ and waste time!
• Example: Find PV of receiving $100 at the end
of year 1, $200 at the end of year 2, $400 at the
end of year 3 and $600 at the end of year 4,
using 10%, and then add all those up, OR...
…or a series of unequal cash flows;
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PV OF UNEVEN
CASHFLOWS
Key Strokes Explanation Display
[ CF ] [ 2nd ] [ CLR WORK ] Clear CF Registers CF0 = 0.00000
0 [ Enter ] Initial Outflow = 0 CF0 = 0.00000
 100 [ Enter ] Enter CF1 C01 = 100.00
 200 [ Enter ] Enter CF2 C02 = 200.00
 400 [ Enter ] Enter CF3 C03 = 400.00
 600 [ Enter ] Enter CF4 C04 = 600.00
[ NPV ] 10 [ Enter ] Enters Interest Rate I= 10.000
[ CPT ] Calculate NPV NPV = 966.53
(PV in this case)
To get FV, [CE/C] (display = 966.53234)
[PV] (enters 966.53234 as PV)
10 [I/Y] (enters 10% interest)
4 [N] (enters 4 years)
[CPT] [FV] (Display = -1,415.10) This is actually a
positive value, if PV is positive, FV is given as negative
CF0= 0, CF1= 100, CF2= 200
CF3= 400, CF4= 600, I = 10%
With TI-BAII+Pro
After NPV, ,
NFV, [CPT],
NFV = 1,415.10

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
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NPV, IRR EXAMPLE
•Assume a project costs $1,000. It will generate
cash flows of $100, $200, $400, $600 for the next
4 years1. The discount rate is 10%. Calculate NPV
and IRR.
•CF0= 1000, CF1= 100, CF2= 200,
CF3= 400, CF4= 600, I = 10%
•NPV = 33.47
•IRR = 8.79%, note NPV < 0, IRR < discount rate.
1Like the previous example, except for initial cost.
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NPV & IRR OF UNEVEN
CASH FLOWS
Key Strokes Explanation Display
[CF] [ 2nd ] [ CLR WORK ] Clear CF Registers CF0 = 0.00
1000 [+/-] [ Enter ] Initial Outflow CF0 = -1000.00
 100 [ Enter ] Enter CF1 C01 = 100.00
 200 [ Enter ] Enter CF2 C02 = 200.00
 400 [ Enter ] Enter CF3 C03 = 400.00
 600 [ Enter ] Enter CF4 C04 = 600.00
[ NPV ] 10 [ Enter ] Enters Interest Rate I = 10.00
[ CPT ] Calculate NPV NPV = -33.47
[ IRR ] [CPT] Calculate IRR IRR = 8.79
To get FV, [CE/C] (display = -33.47)
[PV] (enters -33.47 as PV)
10 [I/Y] (enters 10% interest)
4 [N] (enters 4 years)
[CPT] [FV] (Display = 49.00) This is actually a negative FV
I = 10%, CF0= -1000, CF1= 100,
CF2= 200, CF3= 400, CF4= 600
X
With TI-BAII+Pro
After NPV, ,
NFV, [CPT],
NFV = -49.00

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 11
Viewingand/orCorrectingCashFlow
forinputsforNPVandIRR
AfterinputtingtheCashFlowsfor
anNPVorIRRcalculation,youcan
seethevaluesbygoingbackto
the[CF]keyandusethearrows.
Forexample,
FØ_isusedifthecashflowis
repeatedseveralyearsinarow.
YoucancorrectanCFinputwhen
youfindanerrorbyusingthe
enterkey.Forexample,assume
youentered‐10forCF0whenit
shouldhavebeen‐1000.
[CF] ShowsCFo
[]ShowsCØ1
[]ShowsFØ1
[]ShowsCØ2
Etc…
Key Shows
[CF] CFo =‐10
1000[
⁄][ENTER] CFo=‐1000
Youcanuse thedownarrowsto
findandcorrectanyothercash
flowerrors.
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CashFlows
•Note:ontheexamtheymaytryatrick:
•Assumethecashflowsare
CF0=‐1000,CF1=100,CF2=200,CF3=0,
CF4=400,CF5=500.
•YouMUSTenterCF3as0ortheremaining
cashflowswillbeforthewrongperiodsand
youwillgetthewronganswer!
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CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 12
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Practice Problem
Year S&P
2007 13.5%
2008 -1.2%
2009 -35.6%
2010 32.4%
2011 16.5%
2012 3.8%
Rf3.0%
Calculate the following:
1. Mean
2. Standard Deviation
3. Coefficient of Variation
4. Sharpe Ratio
Similar to example in D.Cary lecture notes.
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Youcanviewyourinputtedvaluesbygoinginto
DATAmodeandthenusingupordownarrows.
TI-BAII+ (and Pro): On Screen
[2ND][Data] X01 0.0000 Opens Input
[2ND][CLR WORK] X01 0.0000 Clears Memories
13.5 [ENTER] X01 = 13.5000 Enters 1st value
1.2 [+/-][ENTER] X02 = -1.2000 Enters 2nd value
35.6 [+/-][ENTER] X03 = -35.6000 Enters 3rd value
32.4 [ENTER] X04 = 32.4000 Enters 4th value
16.5 [ENTER] X05 = 16.5000 Enters 5th value
3.8 [ENTER] X06 = 3.8000 Enters 6th value
[2ND] [STAT] LIN
N = 6.0000 Number of items
x

 4.9000 Mean
Sx = 22.9932 Standard Deviation
You use the two down arrows
as the calculator can use x &
y values for a regression.

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 13
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25
If asked for the Mean
Absolute Deviation: No
shortcut!
Year S&P |S&P‐ Mean|
2007 13.50% 8.60%
2008 ‐1.20% 6.10%
2009 ‐35.60% 40.50%
2010 32.40% 27.50%
2011 16.50% 11.60%
2012 3.80% 1.10%
sum 29.40% 95.4%
Mean 4.90%
median 8.65%
MAD 15.90%
Mean = r = 4.90%
StDev = s = 22.99%
3. Coefficient of Variation = s / r
CV = 22.99% /4.90%
= 4.69
4. Sharpe = (r
 rf) / s
= (4.90% 3.0%) /22.99%
= 0.083
6
GeometricandHarmonicMean
UsingtheStatisticsFunctionforthecalculationisafterthisslide.
•Data:3,3,4,6,22
GeometricMean(ALG)
KEYS DISPLAY
3[]3.0000
3[]9.0000
4[]36.0000
6[]216.000
22[=] 4,752.0000
[yx]5[1/x][=] 5.4372
HarmonicMean(ALG)
KEYS DISPLAY
3[1/x][+]0.3333
3[1/x][+] 0.6667
4[1/x][+] 0.9167
6[1/x][+] 1.0833
22[1/x][=] 1.1288
[]5[=] 0.2258
[1/x] 4.4295
FromD.Cary’s notes,SS2,slides81&84.
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CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 14
•Thenexttwoslidesshowhowtousethebuilt‐
instatisticfunctionstodoGeometricand
HarmonicAveragecalculations.
•I’mnotsuretheyareanyeasier,butthoughtI
wouldincludethemsoyoucancompare.
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UsingtheStatisticsFunction
toCalculateGeometricMean
Keys Display Comments
[2nd][DATA]
[2nd][CLRWORK]
X01 0.0000 ClearsMemories
3[LN][ENTER] X01=1.0986 Convertsto Log,Entersfirstvalue
3[LN][ENTER] X02=1.0986 Convertsto Log,Enterssecondvalue
4[LN][ENTER] X03=1.3863 Convertsto Log,Entersthirdvalue
6[LN][ENTER] X04=1.7918 Convertsto Log,Entersfourthvalue
22[LN][ENTER] X05=3.0910 Convertsto Log,Entersfifth value
[2nd][STAT] LIN Just showsinlinearformat
N=5.0000
x =1.6933 The averageofthelogs
[2nd][e
x] 5.4372 Convertstheaverageofthelogstotheanswer!
•Data:3,3,4,6,22
Note:convertingthenumbers
tologs,calculatingthe
average,thenusingexisthe
sameasmultiplyingthe
numbersandtakingtheroot.
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Probablyeasiertojustmultiplythenumbersandtaketheroot!

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 15
UsingtheStatisticsFunctionto
CalculateHarmonicMean
Keys Display Comments
[2nd][DATA]
[2nd][CLRWORK]
X01 0.0000 ClearsMemories
3[1/x][ENTER] X01=0.3333 Convertstoreciprocal, Entersvalue
3[1/x][ENTER] X02=0.3333 Convertstoreciprocal, Entersvalue
4[1/x][ENTER] X03=0.2500 Convertstoreciprocal, Entersvalue
6[1/x][ENTER] X04=0.1667 Convertstoreciprocal, Entersvalue
22[1/x][ENTER] X05=0.0455 Convertstoreciprocal, Entersvalue
[2nd][DATA] LIN Just showsinlinearformat
N=5.0000 Numberofobservations
x =0.2258 Getsaverageofreciprocals
[1/x] 4.4295 Thereciprocal oftheaverage
reciprocal.TheAnswer!
•Data:3,3,4,6,22
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Viewingand/orCorrecting
forinputswhenusingSTATfunction
Afterinputtingthevalues
foracalculation,youcan
seethevaluesbygoingback
tothe[2nd][DATA]keyand
usethearrows.For
example,
Youcancorrectaninput
valuewhenyoufindan
errorbyusingtheenterkey.
Forexample,assumeyou
entered30forXØ1whenit
shouldhavebeen3.
[2nd][DATA]ShowsXØ1
[]ShowsYØ1
[]ShowsXØ2
[]ShowsYØ2
Etc…
Key Shows
[2nd][DATA]XØ1=30
3[ENTER] XØ1=3
Youcanuse thedownarrowsto
findandcorrectanyothererrors.
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“Y”valuesnotusedformostoflevel1!

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 16
CFA Society Los Angeles
Tree Diagram
• Assume there is a 60% probability that interest
rates will decrease and if they do, there is a 25%
chance that EPS = $2.60 and a 75% chance that
EPS = $2.45.
• Also, there is a 40% probability that interest rates
will be stable and if so, there is a 60% probability
that EPS = $2.20 and a 40% probability that EPS
= $2.00
•Note: Actual calculator steps included following
next slide.
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Example from Level I, SS 2, Reading 8
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Figure 8-2
• Overall Expected Value:
0.6 ×(0.25 ×2.60 + 0.75 ×2.45)
+ 0.4 ×(0.6 ×2.20 + 0.4 ×2.00) = $2.34
• Note: 0.6 ×2.4875 + 0.4 ×2.12 = $2.34
EPS = $2.60
25%
75%
60%
40%
EPS = $2.45
EPS = $2.20
EPS = $2.00
Expected Value
if rates decrease:
0.25 ×2.60
+ 0.75 ×2.45
= $2.4875
Expected Value
if stable rates:
0.6 ×2.20
+ 0.4 ×2.00
= $2.12
32

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 17
CFA Society Los Angeles
33
DECISION TREES
Keys (Using Memories) Display Comments
0.60 x 0.25 x 2.60=[STO][1] 0.3900 Top Branch
0.60 x 0.75 x 2.45=[STO][2] 1.1025 2nd Branch
0.40 x 0.60 x 2.20=[STO][3] 0.5280 3rd Branch
0.40 x 0.40 x 2.00=[STO][4] 0.3200 Bottom Branch
[RCL][1]+[RCL][2]+
[RCL][3]+[RCL][4]= 2.3405 Answer
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Note: Quick check for reasonableness, values between 2.60 and
2.00, answer is about in the middle, that is reasonable!
• The next slide shows how to do this using the ‘1-V’ (1 Variable)
function as part of the DATA/STAT functions. For this calculation I
think using the memories above is probably faster and simpler.
• I include the “1-V” method both as an alternative and so you can
see it being used.
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34
Keys (Using STAT) Display
[2nd][DATA]
[2nd][CLR WORK] XØ1 = 0.0000 Clear Memories
2.60[ENTER] XØ1 = 2.6000 Enters XØ1
60x0.25=[ENTER] YØ1 = 15.0000 Combined Probability for #1
2.45[ENTER] XØ2 = 2.4500 Enters XØ2
60x0.75=[ENTER] YØ2 = 45.0000 Combined Probability for #2
2.20[ENTER] XØ3 = 2.2000 Enters XØ3
40x0.60=[ENTER] YØ3 = 24.0000 Combined Probability for #3
2.00[ENTER] XØ4 = 2.0000 Enters XØ4
40x0.40=[ENTER] YØ4 = 16.0000 Combined Probability for #4
[2nd][STAT] LIN
Repeat [2nd][SET] until
1-V appears 1-V Go into 1-V mode
n = 100.0000 To represent 100%
x = 2.3405 The answer
You can also use the DATA/STAT function in the ‘1-V’ mode, Since there
are two probabilities for each branch, the “Y” values must be calculated
with “% x decimal = 60 x 0.25 = 15” to get the right input.

CFALAReview:TipsforusingtheTIcalculator 2/9/2015
ByDavidCary 18
Factorial,Combinations,
andPermutations
•NFactorial(N!)iswhenyoumultiply
Nx(N‐1)x(N‐2)x…x2x1=N!
•Thereisabuiltinfunctioninyourcalculatortodothis:
[2nd][x]=[x!],Toget5!:5[2nd][x!]=120
•Thiscanbeusefulforcombinationcalculations:
Toselectasubsetof3itemsoutof5:
5C3=5!/((5‐3!)(3!))=10
YourTIhasabuiltinfunctionforthis:[2nd][+]=[nCr]
5C3=5[2nd][nCr]3[=]10
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Factorial,Combinations,
andPermutations
•Thiscanalsobeusefulforpermutationcalculations:
Toselectandrankasubsetof3itemsoutof5:
5P3=5!/(5‐3!)=60
YourTIhasabuiltinfunctionforthis:[2nd][‐]=[nPr]
5P3=5[2nd][nPr]3[=]60
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