There are 2 groups A and B in a class. A consists of six boys and five girls whereas B consists of
five boys and six girls. They plan a social activity team of five boys and five girls such that five
persons are selected from each of the two groups with atleast two boys and two girls from each
group. In how many ways can this be done?
A. 67600
B. 40000
C. 22500
D. 62500
Answers
Given : 2 group A and B . A consists of six boys and five girl whereas B consist of five boys and six girls
they plan a social activity team of five boys and five girls such that five persons are selected from each of the two groups with atleast two boys and 2 girls from each group
To Find : Number of Ways
Solution:
GA - 6 Boys , 5 Girls
GB - 5 Boys , 6 Girls
5 Boys & 5 Girls to be selected
5 persons are selected from each of the two groups with atleast 2 boys and 2 Girls from each group
There are two possibilities
3 boys and 2 Girls from GA & 2 boys and 3 Girls from GB
or
2 boys and 3 Girls from GA & 3 boys and 3 Girls from GB
3 boys and 2 Girls from GA = ⁶C₃.⁵C₂ = 200
2 boys and 3 Girls from GB = ⁵C₂.⁶C₃ = 200
200 x 200 = 40000
2 boys and 3 Girls from GA = ⁶C₂.⁵C₃ = 150
3 boys and 2 Girls from GB = ⁵C₃.⁶C₂ = 150
150 x 150 = 22500
Total Ways = 40000 + 22500 = 62500
option D is correct
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