Question

A team of 5 members is to be formed from 5 men and 6 women . in how many ways can this be done if the team should consist of : (1) atleast 3 women (2) atmost 3 women​

Answer 1

A team of 5 members is to be formed from 5 men and 6 women. Ways of this to be done if the team should consist of :

1. Atleast 3 women

There are three cases in first part.

• 3 women + 2 men

• 4 women + 1 man

• 5 woman

Case 1 : total way to select 3 women out of 6 and 2 men out of 5 is

6C3 + 5C2 = 30

Case 2 : selection of 4 women and 1 man

6C4 + 5C1 =20

Case 3 : selection of 5 women

6C5 = 6

2. Total ways = 30 + 20 + 6 = 56

3. At most 3 women

There are total four cases

Case 1 : 3 women and 3 men

6C3 + 5C3 = 30

Case 2 : 2 women and 3 men

6C2 + 5C3 = 25

Case 3 : 1 women and 4 men

6C1 + 5C4 = 11

Case 4 : 5 men

5C5 = 1

4. Total ways = 67