Question

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?

Answer 1

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