Question

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​

Answer 1

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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