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 : [2025]

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Solution

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 : [2025]

1 9100

2 8925

3 8750

4 8575

Ans.
(2)

Group A : 7B and 3G

Group B : 6B and 5G.

The number of ways of inviting 4 boys and 4 girls (5 from Group A and 3 from Group B) is gven by

= (3G + 2B, 1G + 2B) + (2G + 3B, 2G + 1B) + (1G + 4B, 3G + 0B)

$= {}^{3}C_{3} \cdot {}^{7}C_{2} \cdot {}^{5}C_{1} \cdot {}^{6}C_{2} + {}^{3}C_{2} \cdot {}^{7}C_{3} \cdot {}^{5}C_{2} \cdot {}^{6}C_{1} + {}^{3}C_{1} \cdot {}^{7}C_{4} \cdot {}^{5}C_{3} \cdot {}^{6}C_{0}$

= 1575 + 6300 + 1050 = 8925.

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