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(D) Let the number of questions chosen from sections $A, B,$ and $C$ be $n_1, n_2,$ and $n_3$ respectively,such that $n_1 + n_2 + n_3 = 5$,where $n_i

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$2250$

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(D) Let the number of questions chosen from sections $A, B,$ and $C$ be $n_1, n_2,$ and $n_3$ respectively,such that $n_1 + n_2 + n_3 = 5$,where $n_i \ge 1$ for $i = 1, 2, 3$.The possible partitions of $5$ into $3$ parts (each $\ge 1$) are:$1) (1, 2, 2)$ in any order: $(1, 2, 2), (2, 1, 2), (2, 2, 1)$.$2) (1, 1, 3)$ in any order: $(1, 1, 3), (1, 3, 1), (3, 1, 1)$.For case $(1, 2, 2)$:Number of ways $= \binom{5}{1} 	imes \binom{5}{2} 	imes \binom{5}{2} = 5 	imes 10 	imes 10 = 500$.Since there are $3$ permutations of $(1, 2, 2)$,total ways $= 3 	imes 500 = 1500$.For case $(1, 1, 3)$:Number of ways $= \binom{5}{1} 	imes \binom{5}{1} 	imes \binom{5}{3} = 5 	imes 5 	imes 10 = 250$.Since there are $3$ permutations of $(1, 1, 3)$,total ways $= 3 	imes 250 = 750$.Total number of ways $= 1500 + 750 = 2250$.

There are $3$ sections in a question paper and each section contains $5$ questions. $A$ candidate has to answer a total of $5$ questions,choosing at least one question from each section. Then the number of ways,in which the candidate can choose the questions,is

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