n! = n × (n – 1) !
The number of permutations of n different things, taken r at a time, where repetition is allowed, is nr
The number of permutations of n objects taken all at a time, where p1 objects are of first kind, p2 objects are of the second kind, …, pk objects are of the kth kind and rest, if any, are all different is \frac{n!}{{p_1}! {p_2}! … {p_k}!}
The number of permutations of n different things taken r at a time, where repetition is not allowed, is denoted by nCr and is given by {^n}C_r = \frac{n!}{r! (n-r)!}, where 0 ≤ r ≤ n.