Question

A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?

Answer 1

There are 9 men and 6 women.

A team of 6 persons is to be formed such that it consists of at least 3 women.

Consider the following table:

	Case I	Case II	Case III	Case IV
	3W 3M	4W 2M	5W 1M	6W –
Number of ways	6C3 × 9C3 = 20 × 84 = 1680	6C4 × 9C2 = 15 × 36 = 540	6C5 × 9C1 = 6 × 9 = 54	1

∴ No. of ways this can be done

= 1680 + 540 + 54 + 1

= 2275

∴ 2275 teams can be formed if the team consists of at least 3 women.