How many different ordered arrangements of the letters a, b, and c are possible? By direct enumeration we see that there are 6; namely, abc, acb, bac, bca, cab, and cba. Each arrangement is known as a permutation. Thus there are 6 possible permutations of a set of 3 objects. This result could also have been obtained from the basic principle, since the first object in the permutation can be any of the 3, the second object in the permutation can then be chosen from any of the remaining 2, and the third object in the permutation is then chosen from the remaining 1. Thus there are possible permutations.
Suppose now that we have n objects. Reasoning similar to that we have just used for the 3 letter shows that there are
different permutations of the n objects.