Question

Six men and six women are to be divided into three different groups, each consisting of two women and two men. In how many ways can this be done? (Answer is 8100)

Explain please.

Answer 1

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

Number of ways in which 2 men and 2 women can be selected for first group = 6C2 x 6C2

= 15 x 15

= 225

Number of ways in which 2 men and 2 men can be selected for second group from remaining 4 men and 4 women = 4C2 x 4C2

= 6 x 6

= 36

Number of ways in which 2 men and 2 men can be selected for second group from remaining 2 men and 2 women = 2C2 x 2C2

= 1

Number of ways in which six men and six women can be divided into three different groups, each consisting of two women and two men = 225 x 36 x 1

= 8100