Get Answers to all your Questions

header-bg qa

In how many ways can the letters of the word ‘ACCOMODATION’ be arranged such that all the vowels occur together?

 

Option: 1

604800


Option: 2

632659


Option: 3

532800

 


Option: 4

504659


Answers (1)

best_answer

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,

\begin{aligned} &\frac{8 !}{2 ! 2 !}=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{2 \times 2}\\ &\frac{8 !}{2 ! 2 !}=10080 \end{aligned}

Vowel A appears twice and O appears thrice, so vowels can be arranged as

\frac{6!}{2!3!}=\frac{6\times 5\times 4\times 3\times 2}{2\times 3\times 2}

\frac{6!}{2!3!}=60

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,

10080\times60=604800

Therefore, the total number of ways to form the letter is 604800.

 

Posted by

Pankaj Sanodiya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE