Question

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

Answer 1

The answer is 15 !

Explanation:
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.

Answer 2

The first one on the list can be any one of 25.

For each of those . . . . .

The 2nd one on the list can be any one of the other 14.

For each of those . . . . .

The 3rd one can be any one of the other 13.

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The total number of different ways to list them is "15 factorial" .

That's written as  " 15 ! ".  It means

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

and it's a big number.

15 !  = 1,307,674,368,000 (rounded to the nearest thousand).