Permutations


The arrangement of \(n\) objects in a specific order using \(r\) objects at a time is called a permutation of \(n\) objects taking \(r\) objects at a time. It is written as \(_nP_r\) and the formula is

\[_nP_r=\frac{n!}{(n-r)!}\]

The number of permutations of \(n\) objects when \(r_1\) objects are identical, \(r_2\) objects are identical,...,\(r_p\) objects are identical, etc. is:

\[\frac{n!}{r_1!r_2!...r_p!}\]

where \(r_1+r_2+...+r_p=n\)