four friends 2 men named john (J) and donald (D) and two women mary (M) and susan (S) have bought four seats in a row for a basketball game. in how many different ways can they be seated can they be seated if the two women are to sit together. If the men sit together and the women sit together Solution When two women sit together, we can take 2 women as one. Now, number of ways of arranging 3 people = 3! = 6 but those 2 women can also change their places,so total number of ways = 6*2 = 12ways When two men and two women sit together, number of ways of arranging 2 pairs = 2!=2 but those two pairs can also interchange seats, so total ways = 2*2*2 = 8 ways.

1. four friends 2 men named john (J) and donald (D) and two women mary (M) and susan (S) have
bought four seats in a row for a basketball game. in how many different ways can they be seated
can they be seated if the two women are to sit together.
If the men sit together and the women sit together
Solution
When two women sit together, we can take 2 women as one. Now, number of ways of arranging
3 people = 3! = 6
but those 2 women can also change their places,so total number of ways = 6*2 = 12ways
When two men and two women sit together, number of ways of arranging 2 pairs = 2!=2
but those two pairs can also interchange seats, so total ways = 2*2*2 = 8 ways