Three of nine astronauts must be selected for a mission

Question

Three of nine astronauts must be selected for a mission. One will be the captain, one will be the navigator, and one will perform scientific experiments. Assuming each of the nine astronauts can perform any of the tasks, in how many ways can a three-person crew be selected so that each person has a different assignment?

Answer 1

Here is a way to think about it: When the selection begins and all 9 astronauts are awaiting their assignment, how many are available to be selected for the first job? 9. After that 1 is selected, how many are available for the 2nd job? 9-1 = 8. How many for the 3rd job? 7. Answer: 9x8x7. Solve and you have your answer!