A committee of 12% is to be formed from 9 women and 8 men in which at least fight women have to be included in a committee then the number of committees in which the women are in majority and men are in majority are respectively

Arun
25757 Points
4 years ago
Dear student

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.

Vikas TU
14149 Points
4 years ago
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 it can be also written as : 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.
The women are in majority in 2016 + 630 + 56 = 2702 ways ,  The men are in majority in 1008 ways.