- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 10. Principles of Counting
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.
B. 360,360
C. 1,575,290
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. |