A debating team consisting of 5 persons is to be chosen from a group of 7 boys and 5 girls. In how many ways can this team be formed so that it contains,
(2) at least one girl
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A debating team of 5 persons has to be created from a group of 7 boys and 5 girls.
The number of ways of creating a team with at least one girl is:
C(5, 1)*C(7, 4) + C(5, 2)*C(7, 3) + C(5, 3)*C(7, 2) + C(5, 4)*C(7, 1) + C(5, 5)*C(7, 0)
= 175 + 350 + 210 + 35 + 1
There are 771 ways of creating a team with at least one girl.
We have 7 boys and 5 girls. So the teams we form can be categorized in to following forms.
- Teams with girls and boys
- Teams with only boys
- Teams with only girls
So except boys only team, every other team has a girl.
Teams containing at least one girl
= Total teams-teams with only boys
So we can have 771 teams at least a girl included.
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