Engineering Board Exam Reviewer · Permutations · medium

In how many ways can the letters of the word COMPUTER be arranged so that the three vowels are together?

  1. 40,320
  2. 720
  3. 4,320
  4. 8,640

Answer

C. 4,320

Solution

Treat the vowels O, U, E as one block: the block plus 5 consonants make 6 objects, arranged in 6!=720 ways. The vowels can be ordered inside the block in 3!=6 ways. Total =720×6=4,320.

More Permutations questions

  1. How many 4-digit numbers can be formed from the digits 0 to 9 if no digit is repeated?
  2. How many distinct arrangements can be made from the letters of the word ENGINEER?
  3. How many distinct arrangements can be made from the letters of the word BANANA?
  4. In how many ways can 7 different books be arranged on a shelf?
  5. Eight contestants compete. In how many ways can first, second, and third place be awarded?
  6. In how many ways can 6 different books be arranged on a shelf?
  7. How many ways can a president, vice president, and secretary be chosen from a club of 10 members (distinct roles)?
  8. In how many ways can the letters of the word "NUMBER" be arranged?
  9. In how many distinct ways can the letters of the word "STATISTICS" be arranged?
  10. How many ways can 4 men and 3 women be seated in a row if the 3 women must sit together?

All Permutations questions