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(D) Let the number of questions chosen from the three sections be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$ for $i = 1, 2, 3$.

Vedclass · Accepted Answer

$2250$

Vedclass · Answer

(D) Let the number of questions chosen from the three sections be $(n_1, n_2, n_3)$ such that $n_1 + n_2 + n_3 = 5$ and $n_i \ge 1$ for $i = 1, 2, 3$.The possible combinations of $(n_1, n_2, n_3)$ are $(3, 1, 1), (1, 3, 1), (1, 1, 3), (2, 2, 1), (2, 1, 2), (1, 2, 2)$.The number of ways to choose the questions is given by the sum of products of combinations:$= ({ }^5C_3 	imes { }^5C_1 	imes { }^5C_1) + ({ }^5C_1 	imes { }^5C_3 	imes { }^5C_1) + ({ }^5C_1 	imes { }^5C_1 	imes { }^5C_3) + ({ }^5C_2 	imes { }^5C_2 	imes { }^5C_1) + ({ }^5C_2 	imes { }^5C_1 	imes { }^5C_2) + ({ }^5C_1 	imes { }^5C_2 	imes { }^5C_2)$$= (10 	imes 5 	imes 5) + (5 	imes 10 	imes 5) + (5 	imes 5 	imes 10) + (10 	imes 10 	imes 5) + (10 	imes 5 	imes 10) + (5 	imes 10 	imes 10)$$= 250 + 250 + 250 + 500 + 500 + 500$$= 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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