Question

In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?

Options

• 24

• 36

• 12

• 18

Answer 1

12

Explanation:

There are 5 letters in the word 'IMAGE' and the odd places are 1^st, 3^rd, and 5^th.

Three vowels A, E and I can occupy odd places in 3! ways, and then the 2 consonants can occupy remaining places in 2! ways.

∴ required number of ways = 3! x 2! = 12