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Class 11MathematicsPermutations and CombinationsFundamental principle of countingExpert
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A quiz has (8) multiple-choice questions and each has (4) options. A student must choose option (A) in exactly (3) questions. In how many ways can the answer sheet be filled?

Answer and explanation

Correct answer: (56\cdot3^5)

Choose the (3) questions with (A) in (\binom{8}{3}) ways, then each of the remaining (5) questions has (3) non-(A) choices. The total is (\binom{8}{3}3^5).

Related tags

PermutationsCombinationsCounting PrincipleClass 11ExpertFundamental Principle Of CountingPermutations And CombinationsMathematics
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