### 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.

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
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