Given: 'EQUATION' No. of letters in the word 'EQUATION' = 8 Vowels in the word 'EQUATION' are: A, E, I, O, U. No. of vowels in the word 'EQUATION' = 5 Consider vowels as one group: (A, E, I, O, U), Q, T, N then there are 4 letters which needs to be arranged. As we know that, the number of ways to arrange n distinct things taken all at a time is given by: nPn=n! ∴ No. of ways to arrange 4 letters = 4! ∵ There are 5 vowels in the group formed. So, number of ways to arrange these vowels = 5! ∴ The number of words with or without meaning that can be formed using the letters of the word such that the vowels come together = 4! × 5! = 2880