# Permutations and Combinations

Permutations are all the possible ways in which elements in a set can be arranged, here the order is important while Combinations are very similar to permutations, but here the order is not important. The main difference between both is order.

# Permutations

Where n is the size of the set and k is the size of the subset

Let’s take an example, suppose we have four letters A, I, S, H and we want to arrange them in a pair in order. so, this is the problem of permutation as the order is important in the arrangement.

Permutations of A, I, S, H are: AI, AS, AH, IA, IS, IH, SA, SI, SH, HA, HI, HS

We have n = 4 as it is the size of the set which is (A, I, S, H) and k = 2 as we have to arrange elements in a pair.

Therefore, the total number of permutations for this set is 12.

# Combinations

Where n is the size of the set and k is the size of the subset

Let’s take the same example, suppose we have four letters A, I, S, H and we want to arrange them in a pair where the order is not important. so, this is the problem of combinations as the order is not important in the arrangement.

Combinations of A, I, S, H are: AI, AS, AH, IS, IH, SH

We have n = 4 as it is the size of the set which is (A, I, S, H) and k = 2 as we have to arrange elements in a pair.

Therefore, the total number of combinations for this set is 6.

Hope this helps you in understanding the difference between permutations and combinations :)

Data Scientist