The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

Step-by-step solution

Here, word, 'EQUATION' contains 5 vowels (A, E, I, O , U ) and 3 consonants ( Q , T , N ). Two cases are possible here Case (I): aligned & Number of ways for this arrangement =(3!) (5!) & Case(II): aligned aligned & Number of ways for this arrangement =(3!) (5!) & Total required number of ways =(3!)(5!)+(3!)(5!) & =1440 aligned