How many ways can letters of the word SINGAPORE be arranged

How many ways can letters of the word SINGAPORE be arranged such that the letters SIN appear together and in that order?

Solution

The word given is \"Singapore\".

This word consists of 9 letters without repitition.

Of this Sin should be together. Hence let us take sin together as one letter and other 6 letters as one letter each.

Now we have 7 letters without repitition.

Hence no of ways to arrange these 7 letters = 7!

= 5040 ways.