CFA Practice Question

CFA Practice Question

A portfolio manager has identified three asset classes with 10, 8, and 6 securities respectively. He wants to create a portfolio with only two securities from each asset class. In how many ways can he create his portfolio?
A. 18,900
B. 480
C. 88
Explanation: Since only two securities can be selected from each asset class, there are nC2 ways of creating a portfolio. As there are three asset classes, we have 10C2 x 8C2 x 6C2 = 45 x 28 x 15 = 18,900 ways of creating a portfolio.

User Contributed Comments 18

User Comment
ljscott How do u do this using HP12C??
kirstydebs Please could someone explain this more clearly?
dealsoutlook damn i added them..gotta stop these silly mistakes :( And they had that answer in there too.

Kirstydebs its pretty simple you are required to choose 2 securities from each class and there is no particular order required so you cant use permutations. So you would use nCr. You would "choose" 2 securities from 10, 2 from 8 and 2 from 6.
Therefore answer would be 10C2*8C2*6C2
Hope this helps
SalmaM i added them too!
Analizer I know Dealsoutlook has explained it, but I still can't understand how the arithmetic results in 18,900. Can someone explain in a simple fashion how the answer is derived?
vadklim To Analizer:
10C2 (2 securities from 10 possible) = 45 diffirent variants
8C2 = 28 diffirent variants
6C2 = 15
And then use multiplication rule
haosheng No need to use calculator at all, answer A is the only one is huge enough to satisfy the common sense
MrBruny Guys, check the answer for reading 8, question 17 out of the CFA textbooks. Should explain it.
JHeld 10C2 = 10!/((10-2)!*2!) Do this for each and apply the muli-Rule.
uma85 On TIBA ...

10C2: type 10 on calc,2nd nCr, type 2, type =. Ans= 45.

8C2: type 8 on calc,2nd nCr, type 2, type =. Ans = 28

6C2: type 6 on calc, 2nd nCr, type 2, type =. Ans= 15

multiply all the ans. 45*28*15= 18,900.
pepper in HP:

10 <g><n!> 2 <g><n!> 10<g><LST x> - <g><n!> X /

"-" = minus
"X" = multiply
"/" = divide
boddunah i added them too.
altynai thanks uma85
zeen1 damn fell for it and added them too...
chandsingh Im from a poor maths background so i have been having alot of difficulty figuring out what the symbols and answers above mean. So for those who need a more pedantic calculation here it is: 10c2 = 10!/((10-2)*2) = 1*2*3*4*5*6*7*8*9*10 / ((1*2*3*4*5*6*7*8) *2) = 3628800 / 80640 = 45 etc
Oksanata i added them too!
CalebMast Quite nice that the calculator does all of the work. This could be another that involves way too many computations. uma85 - very helpful explanation.
ajshittu Thank you pepper
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