SOLUTION: In how many ways can 15 basketball players be listed in a program?

Question 614747: In how many ways can 15 basketball players be listed in a program?
Answer by ashipm01(26) (Show Source): You can put this solution on YOUR website!
There are n! ways to permute an n element collection. So for this problem, there are 15 different people and you are looking for all the different orderings, or permutations, of those 15 people. The answer is 15!, but to see why consider the following:

You have 15 slots, each of which will hold one of the names of the players. You need to fill the first slot with some name. It doesn't matter which name, so you have 15 names to choose from.

Next, you need to fill the second slot from any of the remaining players. Since you have already selected one of the names from the previous step, you only have 14 names remaining, so there are 14 ways to fill this slot.

Similarly, you need to fill the third slot. You have used two of the names from the previous two steps, so now you have 13 names to choose from, which means you have 13 ways to fill this slot.

This continues for each of the remaining twelve slots. Each slot you have one less name to choose from since each step uses one name.

This can be viewed as the following, where each number represents the way of filling one of the slots:

= 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

=

= 1,307,674,368,000
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