1. A combination lock will open when you select the right choice of three numbers (from 1 to 40, inclusive). How many different lock combinations are possible?
2. A combination lock will open when you select the right choice of three numbers (from 1 to 50, inclusive). How many different lock combinations are possible?
3. Four couples reserve seats in one row for a concert. In how many different ways can they sit when
(a) There are no seating restrictions?
(b) The two members of each couple wish to sit together?
4. In how many orders can four girls and four boys walk through a doorway single file when
(a) There are no restrictions?
(b) The girls walk through before the boys?
5. In how many ways can five children posing for a photograph line up in a row?
6. In how many ways can six people sit in a six-passenger car?