Ques. 1JEE Main 2025, 24 January (Evening Shift)
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 :
- 8925
- 9100
- 8575
- 8750
Answer
(1) 8925
Solution
Let A give x boys, y girls (x+y=5); then B gives 4-x boys and 4-y girls.
A has only 3 girls and 4-x 0 (x,y)=(2,3),(3,2),(4,1)
(2B, 3G): 7 C2 3 C3 6 C2 5 C1=21 1 15 5=1575
(3B, 2G): 7 C3 3 C2 6 C1 5 C2=35 3 6 10=6300
(4B, 1G): 7 C4 3 C1 6 C0 5 C3=35 3 1 10=1050
Total =1575+6300+1050=8925
Answer: (1)