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(D) The student needs to select $10$ questions in total,with at least $4$ from section-$A$ ($8$ available) and at least $3$ from section-$B$ ($6$ avai

Vedclass · Accepted Answer

$986$

Vedclass · Answer

(D) The student needs to select $10$ questions in total,with at least $4$ from section-$A$ ($8$ available) and at least $3$ from section-$B$ ($6$ available). Possible combinations $(A, B)$ are: $(i)$ $4$ from $A$ and $6$ from $B$: $\binom{8}{4} 	imes \binom{6}{6} = 70 	imes 1 = 70$ (ii) $5$ from $A$ and $5$ from $B$: $\binom{8}{5} 	imes \binom{6}{5} = 56 	imes 6 = 336$ (iii) $6$ from $A$ and $4$ from $B$: $\binom{8}{6} 	imes \binom{6}{4} = 28 	imes 15 = 420$ (iv) $7$ from $A$ and $3$ from $B$: $\binom{8}{7} 	imes \binom{6}{3} = 8 	imes 20 = 160$ Total ways $= 70 + 336 + 420 + 160 = 986$.

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