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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:

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a

8925

b

9100

c

8575

d

8750

answer is C.

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Detailed Solution

Question Image

C-I (3G & 2B) & (1G & 2B)
C-II (2G & 3B) & (2G & 1B)
C-III (1G & 4B) & (3G & 0B)
Total = C-I + C-II + C-III
$=^{7} C_{2} \cdot^{3} C_{3} \cdot^{6} C_{2} \cdot^{5} C_{1} +^{7} C_{3} \cdot^{3} C_{2} \cdot^{6} {C_{1}}^{5} C_{2} +^{7} C_{4} \cdot^{3} C_{1} \cdot^{6} C_{0} \cdot^{5} C_{3} = 8925$

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