C n r n. Or we could do it this way. A formula for the number of possible combinations of r objects from a set of n objects.
The number of combinations of n distinct objects taken r at a time is.
The first choice allows us n options the second choice allows us n 1 options the third choice allows us n 2 options and so on all the way down to 1. The number of k-combinations for all k is the number of subsets of a set of n elements. The number of combinations is the number of ways to arrange the people on the chairs when the order does not matter. So the formula for the number of permutations is n n-k.