Question

In how many different ways can the letters of the word passenger be arranged such that the two s never occur together?

Answer 1

Hope you are having a good day.

Answer 2

Answer:

The answer to the given question is 70560

Step-by-step explanation:

The word PASSENGER has 9 letters. There are 2 'S's, 2 'E's which are repeating. Other letters are distinct

Total number of arrangements possible with these letters = 9! / ( 2! * 2! ) = 90720

Now,

We can count the arrangements in which all the 'S's are together.

For the same, group all the 2 'S's and consider it as a single packet.

So now there are 8 letters in which

2 'E's are there

Therefore,

Total number of such arrangements possible = 8! / 2!

= 20160

Therefore,

The number of ways in whichthe letters of the word passenger be arranged such that the two s never occur together =

90720 - 20160 = 70560

Hence,

The answer to the given question is 70560