# 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.

$\begin{array}{l}\text{Given total question in each group is}\ 6.\\ \text{He is required to choose only}\ 5\ \text{at most from each and he need to solve}\ 7\ \text{question out of}\ 12.\\ \text{So, the number of ways he can choose}\ 7\ \text{question}=\left(^6C_5.^6C_2\right)+\left(^6C_4.^6C_3\right)+\left(^6C_3.^6C_4\right)+\left(^6C_2.^6C_5\right)\\ =\left(6\times15\right)+\left(15\times20\right)+\left(20\times15\right)+\left(15\times6\right)\\ =780.\end{array}$

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