Multiple choice

How many 6-letter words (with or without meaning) can be formed using all the letters of the word "MATTER", ensuring that vowels are not together?

  1. 60

  2. 120

  3. 240

  4. 480

  5. 520
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total letters: M, A, T, T, E, R (6 letters, 2 T's). Vowels: A, E. Consonants: M, T, T, R. Arrange consonants: 4! / 2! = 12 ways. Gaps for vowels: 5. Choose 2 gaps for 2 vowels: 5P2 = 20. Total = 12 * 20 = 240.

AI explanation

The word MATTER has 6 letters with vowels A and E, and consonants M, T, T, R where T repeats twice. Using the method of gaps, the 4 consonants can be arranged in 4!/2! = 12 ways. These 4 consonants create 5 gaps (including the ends), and to ensure the 2 vowels are never together, we choose 2 of these 5 gaps to place the vowels, which can be done in 5P2 = 20 ways. Multiplying the consonant arrangements by the vowel placements gives 12 * 20 = 240.

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