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  • A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions.

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions.

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eginarrayl extGiven total question in each group is 6.\ extHe is required to choose only 5 extat most from each and he need to solve 7 extquestion out of 12.\ extSo, the number of ways he can choose 7 extquestion=left(^6C_5.^6C_2 ight)+left(^6C_4.^6C_3 ight)+left(^6C_3.^6C_4 ight)+left(^6C_2.^6C_5 ight)\ =left(6 imes15 ight)+left(15 imes20 ight)+left(20 imes15 ight)+left(15 imes6 ight)\ =780.endarray

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Deependra Verma

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