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(A) The total number of questions is $12$ ($3$ sections $	imes$ $4$ questions each). The candidate must select $5$ questions such that at least one q

Vedclass · Accepted Answer

$624$

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(A) The total number of questions is $12$ ($3$ sections $	imes$ $4$ questions each). The candidate must select $5$ questions such that at least one question is chosen from each section.Possible distributions of $5$ questions across $3$ sections $(A, B, C)$ are:Case $1$: $(2, 2, 1)$ in any order. The number of ways is $3 	imes (^4C_2 	imes ^4C_2 	imes ^4C_1) = 3 	imes (6 	imes 6 	imes 4) = 3 	imes 144 = 432$.Case $2$: $(3, 1, 1)$ in any order. The number of ways is $3 	imes (^4C_3 	imes ^4C_1 	imes ^4C_1) = 3 	imes (4 	imes 4 	imes 4) = 3 	imes 64 = 192$.Total number of ways = $432 + 192 = 624$.

There are three sections in a question paper,each containing $4$ questions. If a candidate has to answer only $5$ questions from this paper without leaving any section,then the number of ways the candidate can make the choice of questions is:

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