Find the number of ways of permuting the letters of the word PICTURE so that
all vowels come together

Explanation

The word PICTURE has 3 vowels `{E, I, U}` and 4 consonants `{C, P, R, T}`
Treat the 3 vowles as one unit. Then we can arrange 4 consonants + 1 unit of vowels in 5! Ways. Now 3 vowels among themselves can be permuted in 3! Ways. Hence the number of permutations in which 3 vowels come together.
`=5! xx3!=120xx6=720` ways.