Number of ways committee of 12 can be formed from 9 women and 8 men in which at least 7 women have to be included in a committee is ______

1008

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2702

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6062

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3000

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Solution

The correct option is B
2702

We can select at least 7 women from following ways

Case3: 7 women + 5 men

Case4: 8 women + 4 men

Cases: 9 women + 3 men

The number of ways in which at least 5 women can be included in a committee = sum of all the cases

= $^{9} C_{7} \times^{8} C_{5} +^{9} C_{8} \times^{8} C_{4} +^{9} C_{9} \times^{8} C_{3} = 2016 - 630 + 56 = 2702$ Ways.

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A committee of 12 members is to be formed from 9 women and 8 men. In how many ways can this be done, if at least five women have to be included in a committee?

A committee of 12 is to be formed from 9 women and 8 men in which at least 5 women have to be included in a committee. Then the numbers of committees in which the women are in majority and men are in majority are respectively.

Q. (a) A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to be included in a committee? In how many of these committees (i) the women are in majority (ii) the' men are in majority?
(b) Out of 10 persons (6 males, 4 females), a committee of 5 is formed.
p = number of such committees which include at least one lady.
q = number of such committees which include at least two men.
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Q. A committee of

12

is to be formed from nine women and eight men. In how many ways this be done if at least five women have to be included in a committee? In how many of these committees
a. the women hold majority?
b. the men hold majority?

Q. A committee of

8

persons is to be constituted from a group of

5

women and

7

men. In how many ways can this be done? In how many ways can the committee be formed if it consists of at-least

3

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men? What value is depicted by taking men and women in forming the committee?

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