There are 6 women and 7 men in a group. A committee of 4 is to be chosen from this group.
In how many different ways can a committee be formed that contains three women and one man?

Q. A committee of

5

men and

3

women is to be formed out of

7

men and

6

women. If two particular women are not to be together in the committee, the number of committees formed is

Q. From a group of

8

women and

6

men, a committee of

3

men and

3

women is to be formed. In how many ways can the committee be formed if two of the women refuses to serve together?

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A group contains 6 men and 3 women. A committee is to be formed with 5 people containing 3 men and 2 women. The number of different committees that can be formed is

The correct option is A 6C3×3C23 men can be selected from 6 men in 6C3 waysAnd 2 women can be selected from 3 women in 3C2 ways,Thus by multiplication principle,Number of different committees =6C3×3C2

The correct option is A $^{6} C_{3} \times^{3} C_{2}$
$3$ men can be selected from 6 men in $^{6} C_{3}$ ways
And $2$ women can be selected from 3 women in $^{3} C_{2}$ ways,
Thus by multiplication principle,
Number of different committees $=^{6} C_{3} \times^{3} C_{2}$