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Question
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are never together.
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Solution
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9P9 = 9! ways
∴ n(S) = 9!
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9 P9 = 9! ways
C C C C C C
6 consonants create 7 gaps.
∴ 3 vowels can be arranged in 7 gaps in 7P3 ways. Also 6 consonants can be arranged among themselves in 6P6 = 6! ways.
∴ n(B) = 6! x `""^7"P"_3`
∴ P(B) = `("n"("B"))/("n"("S")`
= `(6! xx""^7"P"_3)/(9!)`
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