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

Asked by lee | 10th Jan, 2014, 07:09: PM

Expert Answer:

There are 12 letters in which T is repeated twice.
 
We need to select 4 letters between P and S from 10 letters in 10C4 = 210 different ways.
 
Since P and S can change their positions, we have 2*10C4 = 2*210 = 420 different ways.
 
The four letters in between P and S can be selected in 4! ways, and hence there
are 4!(420) = 10080 different ways.
 
Consider this 6 letters (P + 4letters + S) as one letter.
 
Since the remaining letters are 6, there are 7 letters in total.
 
So total number of ways = 4!(420)(7!) = 50803200.
 
Since T is repeated twice, the total number of ways = 50803200/2 = 25401600

Answered by Vimala Ramamurthy | 10th Jan, 2014, 10:21: PM

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