Monday, September 15, 2014

How many combinations of 5 players can be created from a group of 9 players? How do I solve this problem?Thanks for any help!

There is a formula for this involving factorials.  A factorial is the starting number (A) times (A-1) times (A-2) etc down to A times 1.  The symbol for factorial is "!"  We use factorials for these problems, because they represent the number of combinations we can get from a group of numbers.

Let's say the total number in the group is X.  The size of each combination is Y.  

The formula for the number of combinations is:

X!  /  Y! (x-y)! 

In your problem, X=9 and y=5.  So, the formula works out to:

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 / (5 x 4 x 3 x 2 x 1) times (4 x 3 x 2 x 1)

9! = 362880

5! = 120

4! = 24

Substituting these amounts, we get: 

362880 / 120 x 24

or

362880 / 2880

or

126 

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