GRE-Style: Combinations Problem

GRE Quantitative · Axiom Academy

EXAMPLE GRE-Style: Combinations Problem Work a committee-selection problem by recognizing it as a combination and applying . A committee of 4 people is to be chosen from a group of 10 candidates . How many different committees can be formed? Nice work — you solved a GRE-style counting problem by recognizing WHEN to use a combination instead of a permutation. A few principles worth keeping for every counting question: A committee is a set, not a sequence: swapping two members doesn't create a new committee, so order does NOT matter — that's the signal to use instead of P(n,r) . The formula: counts the number of ways to choose r items from n without regard to order. Cancel before you multiply: , so the 6! in the denominator cancels, leaving a short product to divide by 4! . On the GRE, the fastest way to classify a counting problem is to ask "if I swap two selected items, is it a different outcome?" No → combination. Yes → permutation.

This is the written version of the interactive lesson above. See the full GRE Quantitative course.