In how many ways can 3boys and 3girls be seated in a row if all boys and all girls must sit side by side?

Answer 1

First we will arrange all the boys and girls together as one group. There are 2 ways to arrange these groups, either boys first and then girls or girls first and then boys.

For each group, the boys can be arranged among themselves in 3! ways and the girls can be arranged among themselves in 3! ways.

Therefore, the total number of ways in which 3 boys and 3 girls can be seated in a row if all boys and all girls must sit side by side is:

2 * 3! * 3! = 2 * 6 * 6 = 72 ways.