數學功課問題 combination?

Primarily the number of combinations
= C(select 5 players out of 10 players as team 1) x C(select remaining 5 players as team 2)
= 10C5 x 5C5

However, by considering symmetry, when the same two groups of players swapped team, this is still regarded as the same combination when team number is not being taken care of. Thus, we have to divide the primary number of combinations by 2 to avoid double counting.

The number of team combinations
= (10C5 x 5C5) / 2
= (10x9x8x7x6/5x4x3x2x1) x 1 / 2
= 252/2
= 126