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Question
If the letters of the word ASSASSINATION are arranged at random. Find the probability that four S’s come consecutively in the word
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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 4 S’s come consecutively in the word, then arrangement may be as follows:
`(SSSS)/(1 "Group") (A A AI I N N T O)/(9 "others")`
∴ Number of words when all S’s are together = `(10!)/(3!2!21)` and the total number of word formed from the words
ASSASSINATION = `(13!)/(3!4!2!!)`
∴ Required probability = `((10!)/(3!2!2!))/((13!)/(3!4!2!2!))`
= `(10!)/(3!2!2!) xx (3!4!2!2!)/(13!)`
= `(10!4!)/(13!)`
= `(10! xx 4 xx 3 xx 2)/(13 xx 12 xx 11 xx 10!)`
= `2/143`
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