If the letters of the word 'REGULATIONS' are arranged at random, then the probability that there will be exactly 4 letters between R and E is

Total number of ways of arranging 11 letters = (11)! ---------- (1) Selection of 4letters to be placed between R and E from the remaining 9 =9C4 These 4letters can be permuted in 4! ways. Now permutation of R and E can be interchanged in 2! ways. ∴ Number of favourable ways =9C46!2!------2 Hence, required probability =11! 9C46!2!