In how many ways can the word ‘ESPECIALLY’ be arranged such that the vowels always come together?
In how many ways can the word ‘ESPECIALLY’ be arranged such that the vowels always come together? Correct Answer 30240
The word ‘ESPECIALLY’ has 10 letters. We have to consider the vowels (EEIA) as 1 letter. Now, we have SPCLLY and (EEIA) i.e., 7(6 + 1) letters. In SPCLLY there are 1 S, 1 P, 1 C, 2L’s and 1 Y. Number of ways we can arrange these letters = 7! / 2! = 2520. There are 4 vowels, can be arranged = 4! / (2!)(1!)(1!) = 12. Number of ways we can arrange so that vowels can come together = (2520 * 12) = 30240.