Permutation online calculator - What is a permutation? How can we calculate nPk?

The P command calculates the permutation (nPk). The n is the number of all given items and k is the number of what you select from them. Choosing 5 cards from 13 cards and sorting has 13P5 patterns.

If you input P 5 2 in the search form above and the calculator outputs 10 as follows.


The first and second number represents n and k respectively. Both are separated by a space and must be positive integers or 0. The P is a command and capital letter.

How to calculate the permutation manually

7P3 means how many patterns choosing 3 items from 7 items and then sorting. Now we name 7 items A, B, C, D, E, F, G and think about choosing 3 items and sorting them. For example, there are the patterns like CAE, DEG, BFA. As CAE, "C" is in the first place, "A" in the second place, "E" in the third place.

  • 1st C
  • 2nd A
  • 3rd E

One letter of 7 letters is put in the first place. After that, one letter of 6 letters is put in the second place because one letter had already been put in the first place. Then one letter of 5 letters is put in the last place. So there are 7 × 6 × 5 = 210 patterns in choosing and sorting.