Question

A group of 7 has to be formed from 6 boys and 4 girls. In how many ways a group can be formed if boys are in the majority in this group?

Answer 1

Number of boys = 6

Number of girls = 4

Number of members in the group = 7

One putting boys in the majority in the group

We have to choose in the following ways :

4 boys + 3 girls

5 boys + 2 girls

6 boys + 1 girls

Number of ways choosing 4 boys and 3 girls

= ⁶C₄ × ⁴C₃

Number of ways choosing 5 boys and 2 girls

= ⁶C₅ × ⁴C₂

Number of ways choosing 6 boys and 1 girl

= ⁶C₆ × ⁴C₁

Required number of ways forming the group

Hence, the group can be formed in 100 ways.