Question

Find the number of different seven letter words that can be formed using the letters R, E, M, A, I, N and S such that odd places are occupied by only vowels and even places are occupied by only consonants.

• A. 4684
• B. 5184
• C. 5684
• D. 6184

Answer 1

The correct option is B 5184

There are 4 consonants and 3 vowels in it and there are 4 odd places and 3 even places.
We have to arrange 3 vowels in 4 odd places and it can be done if and if only repetition is allowed.
Number of ways 3 vowels can occur in 4 different places $=3\times 3\times 3\times 3=81$
Number of ways 4 consonants can occur in 3 different places $=4\times 4\times 4=64$
Therefore, total number of ways possible $=81\times 64=5184$