A student has to answer 10 out of 13 question | vedclass

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Question

(C) The student must select $10$ questions out of $13$ such that at least $5$ are from the first $6$ questions. This implies two possible cases:Case $

Vedclass · Accepted Answer

$161$

Vedclass · Answer

(C) The student must select $10$ questions out of $13$ such that at least $5$ are from the first $6$ questions. This implies two possible cases:Case $I$: Selecting $5$ questions from the first $6$ and $5$ questions from the remaining $7$.Number of ways $= {}^{6}C_{5} 	imes {}^{7}C_{5} = 6 	imes 21 = 126$.Case $II$: Selecting $6$ questions from the first $6$ and $4$ questions from the remaining $7$.Number of ways $= {}^{6}C_{6} 	imes {}^{7}C_{4} = 1 	imes 35 = 35$.Total number of ways $= 126 + 35 = 161$.

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

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