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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

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a
11! 9C46!
b
12! 9C56!2!
c
11! 9P46!2!
d
11! 9C46!2!

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detailed solution

Correct option is D

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!


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