Question

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´?

• A. 240
• B. 120
• C. 60
• D. 360

Answer 1

Answer: (A)

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 $=4{\times }^5{P}_3$
$=4\times \frac{5!}{\left(5-3\right)!}=\frac{4\times 5\times 4\times 3\times 2}{2}=240$