Permutations and Arrangements

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Calculate

Example: a 4-digit password, all digits different, chosen from 0 to 9. How many are there? And if digits could repeat? Change the values and the kind of count to work out your own case.

Items available n Items chosen k Kind of count

Step by step

What each term means

Arrangement (A(n, k)): How many ordered sequences of k different items can be formed from n items: podiums, passwords without repeats, queues.
Factorial of n (n!): Every possible order of the n items: n · (n − 1) · … · 1. When k = n, the arrangement is the permutation, n!.
Factorial of What Is Left ((n − k)!): Cancels the factors of the items left out. What remains is n · (n − 1) · … · (n − k + 1): n options for the first position, one fewer for each next one.