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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. (a) The women are in majority? (B) The men are in majority?

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.
(a)  The women are in majority?
(B) The men are in majority?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Hello Student,
Please find the answer to your question
Given that there are 9 women and 8 men. A committee of 12 is to be formed including at least 5 women. This can be done in the following ways.
= 5W and 7M or 6W and 6M
Or 7W and 5M
Or 8W and 4M
Or 9W and 3M
No. of ways of forming committee is
= 9 C5 x 8 C7 + 9 C6 x 8 C6 + 9 C7 x 8 C5 + 9 C8 x 8 C4 + 9 C9 x 8 C3
= 9. 8. 7. 6 / 4 .3. 2. 1 x 8 + 9. 8. 7/3. 2. 1 x 8. 7/2. 1 + 9. 8/2. 1 x 8. 7. 6/3. 2. 1
+ 9 x 8. 7. 6. 5/4. 3. 2. 1 + 1 x 8. 7. 6/3. 2. 1
= 126 x 8 + 24 x 28 + 36 x 56 + 9 x 70 + 56 = 6062 ways.
(a) The women are in majority in 2016 + 630 + 56 = 2702 ways
(b) The men are in majority in 1008 ways.

Thanks
navjot kalra
askIITians Faculty

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