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

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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

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.**

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