The number of permutations of n things taken r at a time if 3 particular things always occur is

Explanation

`r !^(n-3) C_r-3`
Here, we have to permute `n` things of which 3 things are to be included.

So, only the remaining `(n-3)` things are left for permutation, taking `(r-`
3) things at a time. This is because 3 things have already been included.

But, these `r` things can be arranged in `r` ! ways.

`therefore` Total number of permutations `=r !^(n-3) C_r-3`