Question

A group consists of 8 men and 5 women. Find the number of committees of 5 persons that can be formed, if committee consists of at least 3 women.

Answer 1

Answer:

321

Step-by-step explanation:

Hi,

Given there are 8 men and 5 women,

Required to form a committee of 5 persons consisting of at least 3 women

We have the following cases

Case 1 : Committee consisting of 2 Men and 3 Women

  We can select 2 men out of 8 in ⁸C₂ ways = 28 ,

  We can select 3 women out of 5 in ⁵C₃ ways = 10

  Total number of ways of choosing 2M and 3W would be 28*10 = 280

Case 2 : Committee consisting of 1 Men and 4 Women

  We can select 1 men out of 8 in ⁸C₁ ways = 8 ,

  We can select 4 women out of 5 in ⁵C₄ ways = 5

  Total number of ways of choosing 1M and 4W would be 8*5 = 40

Case 3 : Committee consisting of 0 Men and 5 Women

    We can select 5 women out of 5 in ⁵C₅ways = 1, i.e., selecting all the

   women so total number of ways of choosing 0M and 5W would be 1

Since any one of the above mentioned case is possible, so total

number of committees that can be formed are 280 + 40 + 1 = 321.

Hope, it helps !