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 3 M's and 1 X).To ensure no two consonants occur together, we must place them in the gaps created by the vowels.First, arrange the vowels: A, I, U. There are 3! ways to arrange these distinct vowels.These arrangements create 4 possible gaps for the consonants: _ V _ V _ V _We have 4 consonants (M, M, M, X) and 4 gaps. To ensure no two consonants are together, each consonant must occupy a unique gap.The number of ways to arrange the 4 consonants (M, M, M, X) is 4! / 3! (since there are 3 identical M's) = 4.So, the total number of words is (Arrangements of vowels) × (Arrangements of consonants in gaps) = 3! × (4! / 3!) = 6 × 4 = 24.Since 4! = 24, option A is correct.
Hint
First arrange the letters that are NOT restricted (the vowels). Then, use the gaps created by these letters to place the restricted letters (the consonants), ensuring they don't sit next to each other.