Given: the word is ‘STRANGE.’

To find: a number of arrangements in which vowels come together

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

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

So, the total number of letters = 6(AE S T R N G)

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 6 things taken all at a time

= P(6, 6)

{∵ 0! = 1}

= 6!

= 6 × 5 × 4 × 3 × 2 × 1

= 720

Two vowels which are together as a letter can be arranged in 2

Ways like EA or AE

Hence, total number of arrangements in which vowels come together = 2 × 720 = 1440