The first place and 15th place are already decided, so we have to find the number of different ways that the <em>other</em> 13 students can line up, in the places from #2 to #14.
2nd place can be any one of 13 people. For each of those . . . 3rd place can be any one of 12 people. For each of those . . . 4th place can be any one of 11 people. For each of those . . . . . . 13th place can be any one of 2 people. For each of those . . . 14th place has to be the one student who is left.
Total number of ways that 13 students can line up in places #2 through #14 is
(13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
That number is called "thirteen factorial". The number is <u>6,227,020,800</u> .
When you write it in math, you write it like this: 13!
