CFA Practice Question

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CFA Practice Question

How many ways are there to include 15 different stocks into 3 different portfolios if one portfolio has 3 stocks, another 5, and another portfolio has 7 stocks.

A. 360
B. 360,360
C. 1,575,290
Correct Answer: B

Use the multinomial formula: [15!]/[3! x 5! x 7!] = 360,360.

User Contributed Comments 11

User Comment
Nancyz 15C3 x 12C5 x 7C7
madhi You need to treat each portfolio as a single case.
Nuta Nancyz' logic is useful for exam speed! Thanks!
Sebgati It also works on the other way : 15C7 x 8C5 x 3C3
dhess0 What does the C stand for in the shortcuts above? I'm missing something.
EminYus Combination on the calculator. nCr
Emily1119 What is 15c3, 12c5, 7c7 come from?
johntan1979 I think they dropped from the sky
Thediceman 15!/(15-3)!*3! chose 3 from 15 no repetition

then there are 12 stocks left for combination
12!/(12-5)!*5! chose 5 from 12 no repetition

the rest of 7 stocks will include in the third portfile.

multiply two possibility.
FozzeyBear this question is not clear, it doesn't say that one stock can't be in multiple portfolios, which would make more sense from a practical perspective
cfastudypl since there are 3 different portfolios, divide 15 by 3 to give you five, then 15P5 gives you 360,360 which the total number of ways you can have for the three portfolios.
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