In how many ways can the letters of the word ‘ACCOMODATION’ be arranged such that all the vowels occur together?
604800
632659
532800
504659
In the word “ACCOMMODATION” there are 13 letters.
Here, there are 6 vowels (i.e. 2 A’s, 3 O’s, and 1 I) and 7 consonants (i.e 2 C’s, 2 M’s, and each of M, D, T, N)
Considering vowels as one letter, the number of letters becomes 8 which can be arranged is given by,
Vowel A appears twice and O appears thrice, so vowels can be arranged as
Hence the required number of ways in which the letters of the word “ACCOMMODATION” be arranged so that all the vowels occur together is given by,
Therefore, the total number of ways to form the letter is 604800.
Study 40% syllabus and score up to 100% marks in JEE