Question

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

Answer 1

In the word 'CORPORATION', take the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO) - 6 consonants and 1 vowel quantity.

So total letters = 7 (2 R's are there and 3 O's are there)

 Required number of ways = $\frac{7!*5!}{2!*3!} =50400\ ways$