Multiple choice

In how many different ways can the letters of the word ‘MATHEMATICS’ be arranged so that the vowels always come together? शब्द ' MATHEMATICS’ के अक्षरों को कितने अलग-अलग तरीकों से व्यवस्थित किया जा सकता है ताकि स्वर हमेशा एक साथ आए?

  1. 120180

  2. 120216

  3. 120320

  4. 120240

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Treating vowels (A, E, A, I) as one unit gives 8 units total. These 8 units can be arranged in 8! = 40320 ways. Within the vowel unit, the 4 vowels with A repeated twice can be arranged in 4!/2! = 12 ways. Total arrangements = 40320 × 12 = 483,840. Since none of the given options (120180, 120216, 120320, 120240) match this result, option E is correct.

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