Codes with exactly one vowel

Using the 26 letters A–Z (with A, E, I, O, U as the vowels), how many 3-letter codes have no repeated letter and contain exactly one vowel?

Show hints (2)+
  1. Choose the vowel's position (3), then the vowel (5), then two distinct consonants in order.
  2. 35(2120)3\cdot 5\cdot(21\cdot 20).

Answer

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6300

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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