Expert: Paul Klarreich - 10/14/2010

Question
there are 10 basketballers in a team.find how many ways they can be split into two eams of 5.
Answer is 126 .how?

Answer
Questioner:   athena
Country:  Australia
Category:  Advanced Math
Private:  Yes  <<< changed.
 
Subject:  permut/combtn
Question:  there are 10 basketballers in a team.find how many ways they can be split into two eams of 5.
Answer is 126 .how?
...............................
In real life, a basketball team needs a center, a power forward, a shooting forward, a shooting guard, and a point guard.  I think, however, you just want to know how many ways you can select 5 players from 10.

that is C(10,5) = 10!/(5!5!) =

10 9 8 7 6
---------- =
5 4 3 2 1

2 9 8 7 6
---------- =
 4 3 2 1

2 9 2 7 6
---------- =
   3 2 1

2 9 2 7
-------
   1

=  252, which is  126 * 2.

HOWEVER, each time you select a 5-man team, you automatically select the other.  for example, picking:

1,3,5,7,9 for the first and 2,4,6,8,10 for the second

is the same as the reverse.  That is why the answer is 126, not 252.