Dr. J’s Guide to Permutations (without Replacement)

Permutations (without replacement) are an ordered set of k elements taken from a set of n elements where elements cannot be repeated. In constructing this set, we have n choices for the first element, (n-1) choices for the second element, and so on until we have (n-k+1) choices for the kth element. Thus the formula for the number of permutations without replacement is n factorial divided by (n-k) factorial. This formula is applied to cross-over clinical trials to determine the number of possible treatment plans and to shuffling a deck of cards to determine how many different arrangements of those cards there are.