Use permutations and combinations to compute probabilities of compound events and solve problems.
Count combinations when choosing a group and order does not matter
Problem
Because the three selected students form an unordered group, calculate \(10C_{3}\) rather than a permutation.
Big Picture
What this problem is really about
A committee is determined by membership rather than listing order. We’ll classify the outcome as an unordered group, apply the combination formula, cancel shared factorial factors, evaluate the remaining quotient, and explain the factorial overcount avoided.
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