Question

(Suppose that a department contains 10 people, 4 men and 6 women.

(i) How many ways are there to form a committee with 6 members, no restrictions? Explain.

(ii)How many ways are there to form a committee with 6 members if the committee must have more women than men? Explain.

Answer 1

Explanation:

Given that there are 10 people 4 men and 6 women

i) No of ways to select 6 members with no restrictions

= 10C6 = 210

ii) If more women than men should be there then we can have any one of the above possibilities

Women, men = (6,0) , (5,1) (4,2)

So No of ways will be sum of these three possibilities

= 6C6(4C0)+(6C5)(4C1)+(6C4)(4C2)

= 1+24+90

=115