In how many ways can the letters of the word "PERMUTATIONS" be arranged if there are always 4 letters between P and S?

Dear Student

Folowing is the solution to your question

 

Consider letter PERMUTATIONS, there are 12 letters

Put 12 dashes:         1 2 3 4 5 6 7 8 9 10 11 12  and number them as done.

Now select 6 consecutive dashes, like if we consider  2nd place till 7th place, on 2nd place and seventh place P and S can be placed and in between 4 places are left.

We can select these consecutive place in 7 ways i.e. 1-6 and 2-7 and 3-8 and so on and multiply by 2! as they can be P and S can interchange their positions

Total ways for P and S= 7x2!

Corrosponding to these ways we can place the other 10 digits in 10 places as

therefore ans =  =  25401600

 

Regards

Team Topper