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Among (16) members, (4) are senior members. A committee of (7) must contain at least (2) senior members. How many committees are possible?

Answer and explanation

Correct answer: (6952)

The number of senior members can be (2), (3), or (4). The sum is (^{4}C_{2}{}^{12}C_{5}+^{4}C_{3}{}^{12}C_{4}+^{4}C_{4}{}^{12}C_{3}=6952).

Related tags

CommitteeAtleastCaseworkCombinationsPermutations And CombinationsMathematicsClass 11 Mcq

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