How many arrangements can be made out of the letters of the word “ MOTHER” taken four at a time so that each arrangement contains the letter ‘m’?

There are six letters in MOTHER, all different, i.e. arrangement can be made out of the letters of the word MOTHER taken four at a time with M present in every arrangement. So, rest 3 letters can be arrangement from 5 letters

So, total number of ways =$4{\times }^5{P}_3$

$=4\times \frac{5!}{(5-3)!}=\frac{4\times 5\times 4\times 3\times 2}{2}=240$