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**CFA Practice Question**

Suppose that you write an investment newsletter. You track 12 stocks, and you classify these stocks into equal-sized categories of buy, sell, and hold. How many different ways can you classify these stocks into those categories?

A. 36,540

B. 34,680

C. 34,650.

**Explanation:**To answer this question, we need the formula for permutations that takes into account different ways to label things. The number of ways that you can arrange n objects so that there are n_1 of one kind, n_2 of another kind, and so on, up to n_k of a kth kind, is found by using the multinomial formula: n! / [(n_1)! * (n_2)! * ... * (n_k)!]. In this case, your equally-sized categories will be 4 of each kind, 12 in all. 12! / (4!*4!*4!) = 34,650.

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**User Contributed Comments**
13

User |
Comment |
---|---|

Birdy101 |
why does the 12nPr4 * 3 calcualtion not work ? |

chamad |
should'nt be 4 out of 12, then 4 out of 8 and then 4 out of 4? |

twotwo |
why 4? aint ther 3 labels |

twotwo |
never mind, got it, equal size category |

chamad |
anyone using BAII? |

grezavi |
So I am guessing these mocks get tougher as we progressed to the next one.... I hope that's what it is :( |

Bparsons |
This is equivalent to 12 nCr 4 x 8 nCr 4 x 4 nCr 4 |

mattg |
@ grezavi: I am hoping so too, my scores were improving and then ... yikes |

jpducros |
Bparson has it right. |

jsubhen |
nice one bparsons |

Mikehuynh |
Thank Bparsons |

acemaj |
Bparson is the man. Only issue is I probably couldn't figure that out intuitively on the exam. |

pigletin |
order does not matter so it's combination first 4 out of 12: 12C4 second 4 out of 8: 8C4 third 4 out of 4: 4C4 495*70*1 |