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How many different committees can be formed from 11 women and 11 men if the committee consists of 4 women and 5 men?

A) 1001
B) 2002
C) 2500
D) 5005

1 Answer

7 votes

Final answer:

To find the number of different committees that can be formed from 11 women and 11 men, where the committee consists of 4 women and 5 men, we use the combination formula. The answer is 152,460.

Step-by-step explanation:

In order to calculate the number of different committees that can be formed from 11 women and 11 men, where the committee consists of 4 women and 5 men, we need to use the concept of combinations. A combination is a selection of items without regard to the order in which they are selected.

The number of different ways to select 4 women from a group of 11 is represented by the combination formula: C(11, 4) = 11! / ((11-4)! * 4!). This evaluates to 330.

The number of different ways to select 5 men from a group of 11 is represented by the combination formula: C(11, 5) = 11! / ((11-5)! * 5!). This evaluates to 462.

Since the women and men must be selected simultaneously, we multiply the number of ways to select women by the number of ways to select men: 330 * 462 = 152,460.

Therefore, the answer is 152,460.

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