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CAT 2022 Slot 2 · Quant · Permutations, Combinations and Sets · medium

In how many ways can the letters of the word COMPUTER be arranged so that all three vowels (O, U, E) always appear together?

Single correct option

In how many ways can the letters of the word COMPUTER be arranged so that all three vowels (O, U, E) always appear together?
  1. A. 2880
  2. B. 4320
  3. C. 5760
  4. D. 40320
Show answer and solution

Answer: (B) 4320

COMPUTER has 8 distinct letters: 3 vowels (O, U, E) and 5 consonants (C, M, P, T, R). Treat the block of 3 vowels as a single unit, giving 6 units (5 consonants + 1 vowel-block) to arrange: 6! = 720 ways. Within the block, the 3 vowels can be arranged among themselves in 3! = 6 ways. Total arrangements = 720 × 6 = 4320.
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Original question written in the CAT 2022 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake