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

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Question

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

Vedclass · Accepted Answer

$276$

Vedclass · Answer

(B) The student must select $10$ questions out of $13$. The first $5$ questions are in one group and the remaining $8$ questions are in another group. The student must select at least $3$ from the first $5$ questions.Case $1$: Select $3$ from the first $5$ and $7$ from the remaining $8$.Number of ways $= {}^{5}C_{3} 	imes {}^{8}C_{7} = 10 	imes 8 = 80$.Case $2$: Select $4$ from the first $5$ and $6$ from the remaining $8$.Number of ways $= {}^{5}C_{4} 	imes {}^{8}C_{6} = 5 	imes 28 = 140$.Case $3$: Select $5$ from the first $5$ and $5$ from the remaining $8$.Number of ways $= {}^{5}C_{5} 	imes {}^{8}C_{5} = 1 	imes 56 = 56$.Total number of ways $= 80 + 140 + 56 = 276$.

$A$ student has to answer $10$ out of $13$ questions in an examination. The number of ways in which he can answer if he must answer at least $3$ of the first $5$ questions is:

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