# Permutations

As we have seen, the arrangements made by taking some or all elements out of a number of things is called a permutation. Permutation implies “arrangement” where “order of the things” is important.The permutations of three things,

*a b*and

*c*, taken two at a time are

*ab, ba, ac, ca, cb*and

*bc*. Since the order in which the things are taken is important,

*ab*and

*ba*are counted as two different arrangements.

The number of permutations of

*n*things taking

*r*at a time is denoted by

*P*

^{n}*.*

_{r}