Problem 15 of 25sta-015
A club has 7 members. In how many ways can 3 of them be chosen to form a committee, if the order in which they are chosen does not matter?
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Solution walkthrough1:33
- Count ordered picks first, then fix the overcount: a committee is the same in any order.
- Pick one at a time: choices, then , then . That is ordered picks.
- One committee, say A, B, C, can be picked in different orders.
- Those ordered picks are one and the same committee, so each committee was counted times.
- Divide out the repeats: committees.
- Traps: still counts order, divides by instead of , and is .