A question paper has two parts A and B which contain 5 and 4 questions respectively. Each question in part A has an alternative. It is required to attempt at least one question from each part. Then the number of ways of attempting the question paper must be ( There is no importance to the order )

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${(^{5} C_{1}^{} +^{5} C_{2}^{} +^{5} C_{3}^{} +^{5} C_{4}^{} +^{5} C_{5}^{})}^{2} (^{4} C_{1}^{} +^{4} C_{2}^{} +^{4} C_{3}^{} +^{4} C_{4}^{})$

$2 {(^{5} C_{1}^{} +^{5} C_{2}^{} +^{5} C_{3}^{} +^{5} C_{4}^{} +^{5} C_{5}^{})}^{2} (^{4} C_{1}^{} +^{4} C_{2}^{} +^{4} C_{3}^{} +^{4} C_{4}^{})$

$(^{5} C_{1}^{} .2 +^{5} C_{2}^{} {.2}^{2} +^{5} C_{3}^{} {.2}^{3} +^{5} C_{4}^{} {.2}^{4} +^{5} C_{5}^{} 2^{5}) (^{4} C_{1}^{} +^{4} C_{2}^{} +^{4} C_{3}^{} +^{4} C_{4}^{})$

$(3^{5} - 1) (2^{4} - 1) - 1$

answer is C.

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Detailed Solution

= $({5_{C}^{}}_{_{1}^{}}^{} .2 + {5_{C}^{}}_{_{2}^{}}^{} {.2}^{2} + {5_{C}^{}}_{_{3}^{}}^{} {.2}^{3} + {5_{C}^{}}_{_{4}^{}}^{} {.2}^{4} + {5_{C}^{}}_{_{5}^{}}^{} 2^{5})$ is the number of ways of answering 1 or 2 or 3 or 4 or 5 from Part – A , where as

$({4_{C}^{}}_{_{1}^{}}^{} + {4_{C}^{}}_{_{2}^{}}^{} + {4_{C}^{}}_{_{3}^{}}^{} + {4_{C}^{}}_{_{4}^{}}^{})$ is number of ways answering 1 or 2 or 3 or 4
from Part B.