Permutations

When the order doesn’t matter, it is a Combination.

When the order does matter it is a Permutation.

“The combination to the safe is 472”. We do care about the order. 724 won’t work, nor will 247. It has to be exactly 4-7-2.

Permutations without repetitions

A permutation, also called an “arrangement number” or “order”, is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself.

Below are the permutations of string ABC.

ABC ACB BAC BCA CBA CAB

Or for example the first three people in a running race: you can’t be first and second.

Number of combinations

n * (n-1) * (n -2) * ... * 1 = n!

Permutations with repetitions

When repetition is allowed we have permutations with repetitions. For example the the lock below: it could be 333.

Number of combinations

n * n * n ... (r times) = n^r

Cheat Sheets

Permutations cheat sheet

Combinations cheat sheet

Permutations/combinations algorithm ideas.

References

• Math Is Fun
• Permutations/combinations cheat sheets