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Permutations and Combinations · Discussion forum

Medium Level Question 2 – answer, explanation & discussion

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Question 2 Back to Exercise

In how many ways can the letters of NUMBER be arranged so that the vowels occupy only odd positions?

  • A 72
  • B 720
  • C 144 Correct
  • D 36
Correct Answer: Option C

Odd positions: 1, 3, 5 → place U and E: 3P2 = 6

Other 4 letters in the remaining 4 places: 4! = 24

6 × 24 = 144

Trap: 72 forgets that U and E can swap.

Answer: 144

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