A chess team of 2 girls and 2 boys is to be chosen from 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.

Please help me solve the question above.. an explanation will be appreciated.
Thanks

Solution

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