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

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(B) The student needs to select $10$ questions out of $13$ with the condition that at least $4$ must be chosen from the first $5$ questions.Case $I$:

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$196$

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(B) The student needs to select $10$ questions out of $13$ with the condition that at least $4$ must be chosen from the first $5$ questions.Case $I$: Selecting $4$ 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 $II$: Selecting $5$ 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 choices $= 140 + 56 = 196$.

$A$ 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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