Answer
3628800
Work Step by Step
You have to find the possible orders for the final program. There are 10 skaters. The 1st skater has 10 choices, the 2nd one has 9, the 3rd one has 8 and so on.....
10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1=3628800.
There are 3628800 possible orders for the final program.