Multiple choice

In how many ways can the letters of the word MICROSOFT be arranged such that all O's always come together?

  1. $362800$
  2. $40320$
  3. $20160$
  4. $10080$
  5. $181440$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

MICROSOFT has 9 letters with 2 O's. Treat both O's as a single unit. Now we have 8 units (7 distinct letters + 1 combined OO unit) to arrange: 8! = 40320 ways. The O's internally can be arranged in 2! = 2 ways. Total = 40320 × 2 = 80640. However, since the O's are identical, we don't multiply by 2!. The answer is 8! = 40320.

Keep practicing — related questions