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Question
If the letters of the word ASSASSINATION are arranged at random. Find the probability that two I’s and two N’s come together
Solution
Total number of word is ASSASSINATION are 13.
Where, we have 3A’s, 4S’, 2I’s, 2N’s, 1T’s and 1O’s.
If 2I’s and 2N’s come together then there are 10 alphabets
Number of words when 2I’s and 2N’s are come together
= `(10!)/(3!4!) xx (4!)/(2!2!)`
∴ Required probability = `((10!)/(3!4!) xx (4!)/(2!2!))/((13!)/(3!4!2!2!))`
= `(4!10!)/(2!2!3!4!) xx (3!4!2!2!)/(13!)`
= `(4!10!)/(13!)`
= `(4 xx 3 xx 2 xx 10!)/(13 xx 12 xx 11 xx 10!)`
= `(4 xx 3 xx 2)/(13 xx 12 xx 11)`
= `2/143`
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