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Question
The letters of the word LOGARITHM are arranged at random. Find the probability that start with vowel and end with ends with consonant.
Solution
There are 9 letters in the word LOGARITHM.
These letters can be arranged among themselves in 9P9 = 9! ways.
∴ n(S) = 9!
Let E be the event that word starts with vowel and ends with consonant.
There are 3 vowels and 6 consonants in the word LOGARITHM.
∴ The first place can be filled in 3 different ways and the last place can be filled in 6 ways.
Now, remaining 7 letters can be arranged in 7 places in 7P7 = 7! ways
∴ n(E) = 3 × 7! × 6
∴ P(E) = `("n"("E"))/("n"("S")`
= `(3 xx 7! xx 6)/(9!)`
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