- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 10. Principles of Counting

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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.

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.

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**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. |