Question

Our basketball team has 10 players. we need to divide into two teams of 5 for an intra-squad scrimmage. in how many ways can we do this without restriction?

Answer 1

1/2 or 10/5

Explanation:

Answer 2

There are 252 ways to divide the 10 players into two teams of 5 without any restriction.

To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,

Using the formula, C(n, k) =
`(n!)/(k!(n-k)!)`

By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.

Where n = 10

k = 5

C(10, 5) =
`(10!)/(5!(10-5)!)`

C(10, 5) =
`(10!)/(5!(5)!)`

C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)

C(10, 5) = 30240/5*4*3*2*1

C(10, 5) = 252 ways

Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.