Ways to Choose 3 Stocks from a Portfolio of 24

How Many Ways Can You Choose 3 Stocks from a Portfolio of 24?

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Question

You run a mutual fund that holds 24 stocks. Each week, you intend to comprehensively review 3 of them. Assuming this is the first week you are doing this, how many ways can you choose 3 from the 24?

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A. B. C. D.

Explanation

The combination, or binomial formula, gives the number of ways that k objects can be chosen from n items, without regard to the order of choosing. The formula is n_C_k = (n choose k) = n! / [k! *(n-k)!]. In this case, we have (24 choose 3) = 24! / [3! * 21!] = (24 * 23 * 22 ) / (6!) = 2,024.