A student is to answer 10 out of 13 questions | vedclass

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Question

(A) Total number of questions $= 13$. Number of questions to be selected $= 10$. Restriction: At least $4$ from the first $5$ questions must be select

Vedclass · Accepted Answer

$196$

Vedclass · Answer

(A) Total number of questions $= 13$. Number of questions to be selected $= 10$. Restriction: At least $4$ from the first $5$ questions must be selected. Case $I$: Exactly $4$ out of the first $5$ questions are selected. Number of ways to select $4$ questions from $5 = {}^{5}C_{4} = 5$. Remaining $10 - 4 = 6$ questions are selected from the last $13 - 5 = 8$ questions in ${}^{8}C_{6}$ ways. Number of ways $= 5 	imes {}^{8}C_{6} = 5 	imes 28 = 140$. Case $II$: Exactly $5$ out of the first $5$ questions are selected. Number of ways to select $5$ out of $5$ questions $= {}^{5}C_{5} = 1$. Remaining $10 - 5 = 5$ questions are selected from the last $13 - 5 = 8$ questions in ${}^{8}C_{5}$ ways. Number of ways $= 1 	imes {}^{8}C_{5} = 1 	imes 56 = 56$. Total number of ways $= 140 + 56 = 196$.

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

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