A committee of 12 persons is to be formedfrom 9 women and 8 men. In ho

1.	A committee of 12 persons is to be formedfrom 9 women and 8 men. In how many wayscan this be done if at least five women have tobe included in a committee? In how many ofthese committees (i) women are in majority (ii)
Answer» 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 =9C5x8C7+9C6x8C6+9C7x8C5+9C8x8C4+9C9x8C3 = 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.

A committee of 12 persons is to be formedfrom 9 women and 8 men. In how many wayscan this be done if at least five women have tobe included in a committee? In how many ofthese committees (i) women are in majority (ii)

Answer»

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

=9C5x8C7+9C6x8C6+9C7x8C5+9C8x8C4+9C9x8C3

= 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.