Question

How many arrangements of the letters in the word TRANCE are there if the vowels must always be together?

Answer 1

`\text{Consider the word TRANCE}\\ \\ \text{there are total 6 letters out of which 2 are vowels A and E.}\\ \\ \text{now since the vowels must be together, so they can be arranged }2! \text{ ways}\\ \\ \text{now if we consider AE as one letter, the rest of 4 letter along with}\\ \text{AE can be arranged in }5! \text{ ways.}\\ \\ \text{hence the total number of arrangements with vowels always together are:}\\ \\ =5!* 2!\\ \\ =120* 2\\ \\ =240`

Total number of arrangements= 240