How many words can be formed by arranging the letters of the word ‘MUMBAI’ so that all M’s come together?
How many words can be formed by arranging the letters of the word ‘MUMBAI’ so that all M’s come together?

Given:

The word \[MUMBAI\]

There are \[6\] letters in the word \[MUMBAI\]out of which \[2\] are \[Ms\] and the rest all are distinct.

So let us consider both \[Ms\]together as one letter, the remaining \[5\]letters can be arranged in \[5!\]Ways.

Total number of arrangements \[=\text{ }5!\]

\[=\text{ }5\times 4\times 3\times 2\times 1\]

\[=\text{ }120\]

Hence, a total number of words formed during the arrangement of letters of word \[MUMBAI\] such that all \[Ms\] remains together equals to \[120\]