Objects always together (String method)

Objects that must always stay together — the 'string' (block) method.

To count the permutations of $n$ distinct objects, taken all at a time, where $m$ specified objects must always be together:

1. Bundle the $m$ specified objects into a single unit (a "string").
2. This leaves $(n-m+1)$ units in total (the string counts as one). Permute these in $(n-m+1)!$ ways.
3. Permute the $m$ objects within the string, in $m!$ ways.
4. By the rule of product, the total is $m!\times(n-m+1)!.$ …