A Committee Of 5 Persons Is To Be Formed From 6 Men And 4 Women. In H

1.	A Committee Of 5 Persons Is To Be Formed From 6 Men And 4 Women. In How Many Ways Can This Be Done When At Least 2 Women Are Included ?
Answer» When at least 2 WOMEN are included. The committee may consist of 3 women, 2 men : It can be done in 4C36C2ways or, 4 women, 1 man : It can be done in 4C46C1ways or, 2 women, 3 men : It can be done in 4C26C3ways. Total number of ways of forming the COMMITTEES = 4C26C3+4C36C2+4C46C1 = 6 x 20 + 4 x 15 + 1x 6 = 120 + 60 + 6 =186. When at least 2 women are included. The committee may consist of 3 women, 2 men : It can be done in 4C36C2ways or, 4 women, 1 man : It can be done in 4C46C1ways or, 2 women, 3 men : It can be done in 4C26C3ways. Total number of ways of forming the committees = 4C26C3+4C36C2+4C46C1 = 6 x 20 + 4 x 15 + 1x 6 = 120 + 60 + 6 =186.

A Committee Of 5 Persons Is To Be Formed From 6 Men And 4 Women. In How Many Ways Can This Be Done When At Least 2 Women Are Included ?

Answer»

When at least 2 WOMEN are included.

The committee may consist of 3 women, 2 men : It can be done in 4C3*6C2ways

or, 4 women, 1 man : It can be done in 4C4*6C1ways

or, 2 women, 3 men : It can be done in 4C2*6C3ways.

Total number of ways of forming the COMMITTEES

= 4C2*6C3+4C3*6C2+4C4*6C1

= 6 x 20 + 4 x 15 + 1x 6

= 120 + 60 + 6 =186.