The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is _____ .

Step-by-step solution

In the word ASSASSINATION , we will treat all the vowels that is AAAIIO as one letter only. Now, we have AAAIIO SSSSNNT This has 8 = ( 7   +   1 ) letters of which S occurs 4 times, and N occur 2 times, Thus, the number of ways of arranging these letters = 8 ! 4 ! 2 ! = 840 . Now, 6 vowels in which A occurs 3   times, and I occur two times, they can be arranged in 6 ! 3 ! 2 ! = 60    ways.  Therefore, required number of ways =   ( 840   ×   60 )   =   5040