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Question

The numbers 1,2,3,4,......n are arranged in a row at random. The probability that the digits 1,2,3,......k(k<n) appear as neighbours in that order is

A
(nk+1)!n!
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B
(nk+1)!(nk)!
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C
(nk+1)!k!n!
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D
(nk+1)!k!(nk)!
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Solution

The correct option is A (nk+1)!n!
Totalnumberofarrangementsofnnumbers=n!Ifwewantknumberstoappearinthespecificorderi.e.1,2,3,...k,thenitformsoneobjectandrestof(nk)numberscanbearrangedinanyorder.Reqd.no.ofarrangements=(nk+1)! (here1added(nk)numbersand1objectof1toknumberswillbearranged)Probability=(nk+1)!n!Option(A)istheanswer.

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