Suppose that n people would like to enter a museum, but the museum only has room for "k" people. First choose which "k" people from among the "n" people will be allowed in. There are formula_1 ways to do this by definition. Now order the "k" people into a single-file line so that they may pay one at a time. There are "k"! ways to permute this set of size "k". Next, order the "n" − "k" people who must remain outside into a single-file line so that later they can enter one at a time, as the others leave. There are ("n" − "k")! ways to do this. But now we have ordered the entire group of n people, something which can be done in "n"! ways. So both sides count the number of ways to order the "n" people. Division yields the well-known formula for formula_1.