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The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits `1,2,3,..,k(n gt k)` appears as neighbours in that order is

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The numbers 1,2,3,.., n are arranged in a random order. The probability that the digits 1,2,3,..,k(n>k) appears as neighbours in that order is A. (n-k)! n! B. n-k+1 .nCk C. n-k .nCk D. k! n! Select the correct answer from above options

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Correct Answer - B The numbers 1,2,3,..n, can be arranged in a row in n! ways. The total number of ways in which the digits 1,2,3,..,k(k<n) occur together is k!(n-k+1)! Hence, required probability = k!(n-k+1)! n! = n-k+1 .nCk

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