Multiple choice

How many distinct words can be formed from the letters of "MATHEMATICS" if all vowels must always be together?

  1. 1,14,240

  2. 1,20,960

  3. 1,16,320

  4. 1,27,340
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

MATHEMATICS has 11 letters: M(2), A(2), T(2), H(1), E(1), I(1), C(1), S(1). Vowels are A, E, A, I (4 vowels). Treating them as one block, we have 8 units (7 consonants + 1 vowel block). Arrangements = (8! / (2! * 2!)) * (4! / 2!) = (40320 / 4) * (24 / 2) = 10080 * 12 = 120,960.

AI explanation

The word MATHEMATICS has 11 letters where M and T are each repeated twice; treating the 4 vowels (A, A, E, I) as a single unit gives 8 total entities to arrange. The number of arrangements for these 8 entities, accounting for the repeated M and T, is 8! / (2! 2!) = 10080. The vowels inside the unit can be arranged in 4! / 2! = 12 ways due to the repeated A, making the total number of distinct words 10080 multiplied by 12, which equals 120960.

Keep practicing — related questions