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

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Question

(B) The student must answer $10$ questions out of $13$. The first $5$ questions are in one group and the remaining $8$ questions are in another group.

Vedclass · Accepted Answer

$196$

Vedclass · Answer

(B) The student must answer $10$ questions out of $13$. The first $5$ questions are in one group and the remaining $8$ questions are in another group.He must choose at least $4$ from the first $5$ questions. This leads to two cases:Case $1$: He chooses $4$ questions from the first $5$ and $6$ questions from the remaining $8$.Number of ways $= ^5C_4 	imes ^8C_6 = 5 	imes 28 = 140$.Case $2$: He chooses $5$ questions from the first $5$ and $5$ questions from the remaining $8$.Number of ways $= ^5C_5 	imes ^8C_5 = 1 	imes 56 = 56$.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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