Solve the following:
The letters of the word 'EQUATION' are arranged in a row. Find the probability that All the vowels are together
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)
= `(4! xx 5!)/(8!)`