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

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(D) The student needs to select $10$ questions out of $13$. The first $5$ questions are in one group and the remaining $8$ questions are in another gr

Vedclass · Accepted Answer

$196$

Vedclass · Answer

(D) The student needs to select $10$ questions out of $13$. The first $5$ questions are in one group and the remaining $8$ questions are in another group.He must answer at least $4$ questions from the first $5$ questions.Case $1$: He selects $4$ 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 selects $5$ 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 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. Then the total number of possible choices available to him is

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