How many words can be formed using the letters of the word EQUATION so that all the vowels are together.

Explanation

Total number of letters = 8.
Number of vowels = 5 and number of consonants = 3
Take the vowels as a single unit
`therefore` Total units `=1+3=4` which can be arranges in 4! way
and 5 vowels can be arranged among themsaelves in 5! ways.
`therefore` Required number of arrangements
`= 4!xx5! =24xx120=2880`