# A chess team of 2 girls and 2 boys is to be chosen from the 7 girls and 6 boys in the chess club. Find the number of ways this can be done if 2 of the girls are twins and are either both in the...

A chess team of 2 girls and 2 boys is to be chosen from the 7 girls and 6 boys in the chess club.
Find the number of ways this can be done if 2 of the girls are twins and are either both in the team or both not in the team.

Thanks

Posted on

Since twins are either chosen both or none we look at them separately. From the rest of the 5 girls we can choose 2 in

`((5),(2))=(5cdot4)/(1cdot2)=10` ways and from twins we can choose in only 1 way. So we can choose 2 girls in 10+1=11 ways.

Similarly we can choose 2 boys from 6 in `((6),(2))=(6cdot5)/(1cdot2)=15` ways.

So we can choose 2 girls and 2 boys in `11cdot15=165` ways.

Posted on

No of Boys=  6    ,No of Girls =7

Team  2 boys  and 2 girls

Cases

(i) Twins are in team

(ii) Twins are not in team

I . Twins are in team

Girls can be selected C(2,2)

Boys can be selected C(6,2)

By Fundamental Principal of counting  ,Total no. of possible selection

= C(2,2) x C(6,2)                  (i)

II Twins are not in Team

Girls can be selected = C(5,2)

Boys can be selected = C(6,2)

By Fundamental Principal of counting  ,Total no. of possible selection

= C(5,2) x C(6,2)                  (ii)

Thus total no. of possible selection of team= C(2,2)xC(6,2)+C(5,2)xC(6,2)

=C(6,2) {C(2,2)+C(5,2)}

=15 x(1+10)

=15 x11

=165