Combinations and Permutations


  • From: Shula Hebden
  • Date: 19 February 1999
  • Subject: nCr and nPr

I do not have an nCr or nPr button on my calculator.

How can I do the calulations 'by hand'?

Maths Help suggests:

Combinations nCr

Use the formula .

For example,
Note how you can "cancel in chunks" top and bottom to simplify the fraction.

Permutations nPr

Use the formula .

For example,

There is an even quicker way if can remember it . . .

nCr is a fraction with r! on the bottom and the same number of whole numbers starting from n multiplied down in steps on 1 on the top.

For example,

Remember to use symmetry to keep the numbers small:
10C6 is the same as 10C4
12C9 is the same as 12C3
15C13 is the same as 15C2 , etc

nPr is found by nCr multiplied by r!

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