Question

In how many ways can the letters of the word ‘ABACUS’ be arranged such that the vowels always appear together.

Answer 1

In the ABACUS, there are 3 vowels -2 A’s and U. 

Number of letters in ABACUS are 6. 

Let us take the vowels as one, so number of letters now = 4 

∴ Number of ways in which vowels occur together = 4! 

But the 3 vowels can rearrange amongst themselves in \(\frac{3!}{2!}\) ways as ‘A’ appears twice. 

Hence, the total number of ways which vowels occur together = 4! × \(\frac{3!}{2!}\) = 72