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# How many different committees of 5 can be formed from 6 men and 4

Question:

How many different committees of 5 can be formed from 6 men and 4 women, if each committee consists of 3 men and 2 women?

Solution:

Each committee consists of 3 men and 2 women. So, we need to select 3

men out of 6 and 2 women out of 4 . The number of ways, 3 men can be selected out of 6 , is $={ }^{6} C_{3}=20$ The number of ways, 2 women can be selected out of 4 , is $={ }^{4} C_{2}=6$ So, the totally $(20+6)=26$ numbers of different committees can be formed.