Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Let group A supply $b$ boys and $5-b$ girls; then B supplies $4-b$ boys and $b-1$ girls. Girls from A $\le3$ gives $b\ge2$, and $b\le4$. $b=2$: $\binom72\binom33\binom62\binom51=1575$. $b=3$: $\binom73\binom32\binom61\binom52=6300$. $b=4$: $\binom74\binom31\binom60\binom53=1050$. Total $=8925$. Answer (3).

Q. Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group $A$ and the remaining 3 from group $B$, is equal to :

Explanation

Reviewed by Dr. Abubacker

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