A student is asked to answer 10 out of 13 que | vedclass

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Question

(C) The student needs to select $10$ questions out of $13$ total questions,with the constraint of selecting at least $4$ from the first $5$ questions.

Vedclass · Accepted Answer

$196$

Vedclass · Answer

(C) The student needs to select $10$ questions out of $13$ total questions,with the constraint of selecting at least $4$ from the first $5$ questions.Case $I$: Selecting $4$ questions from the first $5$ and $6$ questions from the remaining $8$.Number of ways $= {}^{5}C_{4} 	imes {}^{8}C_{6} = 5 	imes 28 = 140$.Case $II$: Selecting $5$ questions from the first $5$ and $5$ questions from the remaining $8$.Number of ways $= {}^{5}C_{5} 	imes {}^{8}C_{5} = 1 	imes 56 = 56$.Total number of choices $= 140 + 56 = 196$.

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

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