If a set contains N elements, and we want to know what are the number of ways we can order them, then there are N choices for the first element, N1 choices for the second element and so on. We can write them as N×(N1)×(N2)××1=N!. Permutation tells us the number of ways we can order the set of N elements.

If there are N elements in a set and we want to know the number of subsets we can make, then we have 2 choices for the first element, i.e. we can either keep it in the subset or won’t keep it in the subset; 2 choices for the second element and so on for all the N elements. Thus we will have 2N subsets from a set containing N elements.

Example 1

What is the probability that six rolls of a six sided die all give different numbers?

Total number of possible outcomes for 6 rolls of a 6 sided dice are 66, 6 for the first, 6 for the second and so on.

Number of elements in the event: 6 options for the first roll, 5 options for the socond roll and so on. So 6×5×4××1=6!

Therefore the probability of 6 rolls of a 6 sided dice all giving different outcome is: 6!66