14 Combinations of 10

<-- Enter Number of Items (n)
<-- Enter Number of Arrangements (r)

The formula for a combination of choosing r unique ways from n possibilities is:
nCr =n!
r!(n - r)!

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 14 and r = 10, we get:
14C10 =14!
10!(14 - 10)!

Remember from our factorial lesson that n! = n * (n - 1) * (n - 2) * .... * 2 * 1

Calculate the numerator n!:
n! = 14!
14! = 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
14! = 87,178,291,200

Calculate the first denominator (n - r)!:
(n - r)! = (14 - 10)!
(14 - 10)! = 4!
4! = 4 x 3 x 2 x 1
4! = 24

Calculate the second denominator r!:
r! = 10!
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
10! = 3,628,800

Now calculate our combination value nCr for n = 14 and r = 10:
14C10 =87,178,291,200
3,628,800 x 24

14C10 =87,178,291,200
87,091,200

14C10 = 1,001

In Microsoft Excel or , you write this function as =COMBIN(14,10)