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 isA. `((n-k)!)/(n !)`B. `(n-k+1)/(.^(n)C_(k))`C. `(n-k)/(.^(n)C_(k))`D. `(k !)/(n!)`

The numbers 1,2,3,.., n are arranged in a random order. The probabilit

1.	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 isA. `((n-k)!)/(n !)`B. `(n-k+1)/(.^(n)C_(k))`C. `(n-k)/(.^(n)C_(k))`D. `(k !)/(n!)`
Answer» 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 lt n)` occur together is `k! (n-k+1)!` Hence, required probability `=(k!(n-k+1)!)/(n!)=(n-k+1)/(.^(n)C_(k))`

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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 isA. `((n-k)!)/(n !)`B. `(n-k+1)/(.^(n)C_(k))`C. `(n-k)/(.^(n)C_(k))`D. `(k !)/(n!)`

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