Question Detail
Question
The number of words which can be formed from the letters of the word MAXIMUM, if two consonants can't occur together is -
Correct Answer
Option A is the correct answer.
Detailed Explanation
The word MAXIMUM has 7 letters: M, A, X, I, M, U, M.Vowels are A, I, U (3 distinct vowels).Consonants are M, X, M, M (4 consonants, with M repeated 3 times).To ensure no two consonants occur together, we must place the vowels first and then arrange the consonants in the spaces created by the vowels.Arrange the 3 distinct vowels (A, I, U): 3! = 6 ways.These vowels create 4 possible spaces for the consonants: _ V _ V _ V _.Now, we need to place the 4 consonants (M, M, M, X) in these 4 spaces.The number of ways to arrange M, M, M, X is 4! / 3! = 4.Total number of words = (Ways to arrange vowels) × (Ways to arrange consonants)= 3! × (4! / 3!) = 6 × 4 = 24.24 is equal to 4!.
Hint
To ensure no two consonants are together, arrange the vowels first and then place the consonants in the gaps created by the vowels. Account for repeated letters.