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Find the probability that the 3Ns come ...

Find the probability that the 3Ns come consecutively in the arrangement of the letters of the word CONSTANTINOPLE.

Text Solution

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The total number of arrangement of the letters of the word ''CONSTANTINOPLE'' is `(14)!//3! 2! 2!`
Since 3 N's are consecutive, then considering all the 3 N's as single letter, the total number of arrangements is `(12)!//2! 2!`
Therefore, required probability is
`=((12)!//(2! 2!))/((14)!//(3! 2! 2!)) = (3!)/(14xx13) = (3)/(91)`
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