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Class 11MathematicsPermutations and CombinationsCombinationsHard
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How many (6)-element subsets of (A={1,2,3,4,5,6,7,8,9,10,11,12,13}) contain (1) but do not contain both (5) and (6) together?

Answer and explanation

Correct answer: (672)

The element (1) is fixed so choose (5) elements from (12). Subtracting (\binom{10}{3}=120) cases containing both (5), (6) gives (792-120=672).

Related tags

CombinationsClass11HardPermutations And CombinationsMathematicsClass 11 Mcq
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