Sum

Solve the following:

The letters of the word 'EQUATION' are arranged in a row. Find the probability that All the vowels are together

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#### Solution

The letters of the word EQUATION can be arranged in 8! ways.

∴ n(S) = 8!

There are 5 vowels and 3 consonants.

A: all vowels are together we need to arrange

(E, U, A, I, O), Q, T, N

Let us consider all vowels as one unit. So, there are 4 units, which can be arranged in 4! ways.

Also, 5 vowels can be arranged among themselves in 5! ways.

∴ n(A) = 4! x 5!

Required probability = P(A)

= `("n"("A"))/("n"("S"))`

= `(4! xx 5!)/(8!)`

= `1/14`

Concept: Basic Terminologies

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