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Nov 2012 p63 q6
2858
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.
Solution
Consider two cases: twins in the team and twins out of the team.
Case 1: Twins in the team
If the twins are in the team, we need to choose 2 boys from 6 and 0 more girls from the remaining 5 girls.
The number of ways to choose 2 boys is given by:
\(\binom{6}{2} = 15\)
Case 2: Twins out of the team
If the twins are not in the team, we need to choose 2 girls from the remaining 5 girls and 2 boys from 6.
The number of ways to choose 2 girls is:
\(\binom{5}{2} = 10\)
The number of ways to choose 2 boys is:
\(\binom{6}{2} = 15\)
Thus, the total number of ways for this case is:
\(10 \times 15 = 150\)
Total number of ways
Adding both cases together, the total number of ways is:
