Given: the word is ‘VOWELS.’

To find: number of words in which vowels always come together

Number of vowels in this word = 2(O, E)

Now, consider these two vowels as one entity(OE together as a single letter)

So, the total number of letters = 5 (OE V W L S)

Formula used:

Number of arrangements of n things taken all at a time = P(n, n)

∴ Total number of arrangements

= the number of arrangements of 5 things taken all at a time

= P(5, 5)

{∵ 0! = 1}

= 5!

= 5 × 4 × 3 × 2 × 1

= 120

Now, 2 vowels which are together as a letter can be arranged in 2! (like OE or EO)

= 2 × 1 = 2 ways

Total number of words in which vowels come together = 2 × 120 = 240