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How do you calculate combinations $C(n, r)$ and permutations $P(n, r)$?

Study flashcard from the deck ACT Mastery: English, Math, Reading & Science.

Answer

$C(n, r) = \frac{n!}{r!(n - r)!}$ (order does not matter); $P(n, r) = \frac{n!}{(n - r)!}$ (order matters).

Explanation

A committee of 3 from 10 is a combination $C(10, 3) = 120$. Electing President, VP, and Secretary is a permutation $P(10, 3) = 720$.

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