The answer you probably want is 5,005.

The team captain can be any of the 15 girls, i.e. 15 choices

The second in command any of the 14 remaining

The third in command any of the 13 remaining

etc

So the number of possible team selections if you care about who is in which position is

15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7

which works out at 1,816,214,400 unique team orders (the mathematical term being permutations).

But, assuming you don't care who has what position each girl has in the team, you need to bear in mind that the number above counts each possible combination multiple times as it counts any combination of 9 girls in all each of their possible orderings.

Given any combination of 9 out of the 15 girls, the number of times each combination gets counted is the number of different ways you can order 9 those 9 girls, which is

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

which is 362,880

So the number of permutations counts each combination 362,880 times.

Divide the number of permutations 1,816,214,400 by 362,880 to find the answer you probably want, which is just

--> 5,005 combinations.

Source My education