Permutations are different no of arrangements. Making words of 4 letters without repetition or with repetition is an example of permutation. Now suppose we have to make a word of 4 letters by taking any 4 letters from 10 letters  A, B, C, D, E, F, G, H, I

__ __ __ __

10 9 8 7

Four places can be filled in 10×9×8×7 ways, which can be written as \(\cfrac{{10 \times 9 \times 8 \times 7 \times 6!}}{{6!}}\), which means \(\cfrac{{10!}}{{(10 - 4)!}}\) and that is written as \(^{10}{P_4}\) 

So   \({}^n{P_r}\) = \(\cfrac{{n!}}{{(n - r)!}}\)= n.(n – 1).(n – 2)….(n – r + 1)

For example permutations of 4 distinct objects out of 20 distinct objects can be written as \({}^{20}{P_4}\)

Example  01: How many integers between 100 and 999 consist of distinct odd digits?