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Question
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement starting with a vowel and end with a consonant
Solution
There are 6 letters in the word MOTHER, which can be arranged amongst themselves in 6P6 = 6! ways
∴ n(S) = 6! = 720
Let D ≡ the event that arrangement starts with a vowel and ends with a consonant
Vowel for the first place can be chosen in 2C1 = 2 ways.
Consonant for the last place can be chosen in 4C1 = 4 ways
The remaining 4 letters can be arranged in 4P4 = 4! = 24 ways
∴ n(D) = 2 × 4 × 24
∴ P(D) = `("n"("D"))/("n"("S"))`
= `(2 xx 4 xx 24)/720`
= `4/15`
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