If the letters of the word REGULATIONS be arranged in such a way that relative positions of the letters of the word GULATIONS remain the same then the probability that there are exactly 4 letters between R and E is

Step-by-step solution

The totals letters in the word REGULATIONS are 11 . There are 11 places corresponding to 11 letters and in these 11 places R and E can be arranged in P 2 11 ways. Now, Total possible cases where only 4 letters are between R and E are 6 as 1 ,   6 ,   2 ,   7 ,   3 ,   8 ,   4 ,   9 ,   5 ,   10 ,   6 ,   11 where the numbers represent the place number and on reversing the order, we get total 12 cases. Hence, the required probability is 12 P 2 11 = 12 × 9 !