The Smith family has 4 sons and 3 daughters. In how many ways can they be seated in a row of 7 chairs such that all 3 girls sit next to each other?
Number the chairs 1, 2, 3, 4, 5, 6, and 7
The girls will be seated together if they're in chairs 1, 2, 3
2, 3, 4
3, 4, 5
4, 5, 6
or 5, 6, 7
unless you arrange the chairs in a circle
and then you can add to the above 6, 7, 1
7, 1, 2
.