A team is to be chosen from 4 girls and 6 boys. The only requirement is that must contain at least 2 girls. How many different teams may be chosen?
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Jawab:
The total number of teams that can be chosen from 4 girls and 6 boys is 10 choose 2, or 45. This is the number of teams that we would have if there were no requirement that the team must contain at least 2 girls.
To find the number of teams that contain at least 2 girls, we can subtract the number of teams with no girls and the number of teams with exactly 1 girl.
The number of teams with no girls is the number of teams that can be chosen from the 6 boys, which is 6 choose 2, or 15.
The number of teams with exactly 1 girl is the number of ways to choose 1 girl from the 4 girls and 1 boy from the 6 boys, which is 4 choose 1 * 6 choose 1, or 24.
Therefore, the number of teams that contain at least 2 girls is:
45 - 15 - 24 = 6
So there are 6 different teams that may be chosen.
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