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Question
If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?
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Solution
Word ALGORITHM has 9 letters.
If GOR remain together, then it will remain together.
∴ Number of letters = ALGOR ITHM = 6 + 1 = 7
Number of words = 7!
And the total number of words from ALGORITHM = 9!
So, the required probability = `(71)/(9!)`
= `(7!)/(9*8*7!)`
= `1/72`
Hence, the required probability = `1/72`.
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