Question

many college honor societies are named using greek letters. if there are 24 letters in the greek alphabet, and only capital letters are used, how many society names can be formed if the letters cannot be repeated?

Answer 1

From 24 total letters available, we're picking 3 (without replacement). The number of ways of doing so is


`P(24,3)=(24!)/((24-3)!)=(24!)/(21!)=12,144`

In other words, we're counting the permutations of 24 objects taken 3 at a time. (Permutations because, presumably, Alpha Beta Gamma is not the same as Gamma Alpha Beta, for instance.)