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Question
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are never together
Solution
There are 6 letters in the word MOTHER, which can be arranged amongst themselves in 6P6 = 6! ways.
∴ n(S) = 6! = 720
Let B ≡ the event that vowels are not together
∴ B = `bar("A")`
∴ P(B) = `"P"(bar"A")`
= 1 – P(A)
= `1 - 1/3`
= `2/3`
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