Question
Download Solution PDFIn how many ways can the word 'CORONAVIRUS' be arranged such that all the vowels come together?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- The ways of arranging n different things = n!
- The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
- The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
- The number of ways for selecting r from a group of n (n > r) = nCr
Calculation:
Given: The word CORONAVIRUS
There are 5 vowels in the word (A, I, O, O, U)
Taking vowels a single group (A, I, O, U) and O repeated two times
They can be arranged within themselves in \(\rm \frac {5!}{2!}\) ways
Now to arrange letters we have (AIOOU), C, R, N, V, R, S
They can be arranged in = \(\rm 7!\over2!\) ways ('R' appear 2 times)
Hence the required arrangement = \(\rm {7!\over2!} \times {5!\over2!}\) = 30 × 7! ways
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