Question

In how many different ways can the letters of the word ‘PRACTICAL’ be arranged so that vowels are never together?

Answer 1

Given word is PRACTICAL

Number of letters in the given word = 9

These 9 letters can be arranged in 9! ways.

Number of vowels in the given word = 3 (I, A, A)

The number of ways of arrangement in which vowels come together is 8! × 3! ways

 

Hence, the required number of ways can the letters of the word 'PRACTICAL' be arranged so that the vowels never come together = 9! - (8! × 3!) ways = 362880 - (40320 × 6) = 362880 - 241920 = 120960 ways.

I hope this helped

@ana205