15! = 15 x 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

15! = 1,307,674,368,000

Calculate (n - r)!:

(n - r)! = (15 - 5)!

(15 - 5)! = 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

Calculate r!:

r! = 5!

5! = 5 x 4 x 3 x 2 x 1

5! = 120

Calculate _{15}C_{5}

_{15}C_{5} =

1,307,674,368,000

120 x 3,628,800

_{15}C_{5} =

1,307,674,368,000

435,456,000

_{15}C_{5} = 3,003

Excel or Google Sheets formula:

Excel or Google Sheets formula:=COMBIN(15,5)

What is the Answer?

_{15}C_{5} = 3,003

How does the Permutations and Combinations Calculator work?

Free Permutations and Combinations Calculator - Calculates the following: Number of permutation(s) of n items arranged in r ways = _{n}P_{r} Number of combination(s) of n items arranged in r unique ways = _{n}C_{r} including subsets of sets This calculator has 2 inputs.

What 2 formulas are used for the Permutations and Combinations Calculator?

What 4 concepts are covered in the Permutations and Combinations Calculator?

combination

a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter _{n}P_{r} = n!/r!(n - r)!

factorial

The product of an integer and all the integers below it

permutation

a way in which a set or number of things can be ordered or arranged. _{n}P_{r} = n!/(n - r)!

permutations and combinations

Example calculations for the Permutations and Combinations Calculator