Question

The letters of the word 'CLIFTON' arc placed at random in a row. What is the chance that two vowels come together?

Answer 1

There are 7 letters in the word `CLIFTON' which can be arranged in 7! ways There are two vowels, namely 1 and 0

Let us consider these two vowels as one letters

So, when the two vowels are clubbed together we have (I, 0) CLFTN

We can arrange six letters in a row in 6! ways

Also, two vowels can be arranged in 2! ways

Hence, required probability $=\frac{6!\times 2!}{7!}=\frac{6!\times 2!}{7\times 6!}=\frac{2}{7}$