Question

Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are never together

Answer 1

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`