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NDA 2024 · PYQ · Permutations and Combinations · easy

How many four-digit natural numbers are there such that all of the digits are even?

  1. A.625
  2. B.500
  3. C.400✓ Correct
  4. D.256

Explanation

Even digits are 0, 2, 4, 6, 8 (5 choices). For a 4-digit number, the first digit cannot be 0, so 4 choices (2,4,6,8). Each of the remaining 3 digits has 5 choices. Total = 4 × 5 × 5 × 5 = 500. Wait, that gives 500. Let me recheck: 4 × 5³ = 4 × 125 = 500. Answer is (b) 500.
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