A group of 18 people have gotten together to play baseball. they will divide themselves into two teams of 9 players each, with one team wearing green uniforms and the other wearing yellow uniforms. in how many ways can this be done?

In this problem, what we can do to solve for the number of ways is to use the combination formula:

nCr = n! / r! (n - r) !

where n is the total number of people and r is the number of person per team.

We can identify two cases in this problem.

1st case: We select the first 9 people for the green team, and the rest of 9 automatically gets to the yellow team therefore the selection is only made on the green team, so

18C9 = 18! / 9! (18 - 9) ! = 48,620

2nd case: We select the first 9 people for the yellow team, and the rest of 9 automatically gets to the green team therefore the selection is only made on the yellow team, so

18C9 = 18! / 9! (18 - 9) ! = 48,620

The total combination is the sum of the two:

total number of ways = 48,620 + 48,620

total number of ways = 97,240