A four member math team is chosen from the math club which has 3 girls and 5 boys How many different teams made up of 2 girls and 2 boys could be chosen?
We are asked to choose a team of 4 members consisting of two
girls and two boys from a math club made up of three girls and five
To choose the girls, we leave one out of the team. There are 3 ways to leave one girl off the team.
To choose the boys, we can choose any one of the 5 for the first and any one of the remaining 4 for the second. However it doesn't matter the order in which we choose them so we divide by 2. This gives us: 5(4)/2 = 10.
This would lead to 3(10) = 30 possible ways to choose the entire team.
Note: This is equivalent to 3 choose 2 * 5 choose 2 = 3 * 10 = 30.
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