Question

In how many different ways can the letters of the word EXAMINATION be arranged so that the vowels always come to gather

Answer 1

Answer:

64,800

Step-by-step explanation:

In how many different ways can the letters of the word EXAMINATION be arranged so that the vowels always come together

Consider the word EXAMINATION. Let us assume all the vowels that is EAIAIO as one letter. Now we get

          XMNTN(EAIAIO) = 5 + 1 = 6

Now we need to arrange 6 letters in which N occurs twice. So number of ways of arranging these letters will be 6! / 2! = 360

Now EAIAIO has 6 letters in which A occurs twice and I  occurs twice and rest are different.

Now number of ways in arranging these letters will be 6! / 2! 2! = 180

So required number of words will be  360 x 180 = 64,800.