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NDA 2026 · PYQ · Probability / Dice · medium

Four dice are rolled. What is the probability that getting at least a total of 23 of the numbers on the dice?

  1. A.1/1296
  2. B.1/432
  3. C.1/324✓ Correct
  4. D.5/1296

Explanation

Sum ≥ 23 with four dice (max 24). Sum = 24: (6,6,6,6), 1 way. Sum = 23: one die shows 5, three show 6: C(4,1) = 4 ways. Total = 5 ways. Probability = 5/1296. Hmm, but answer (c) is 1/324 = 4/1296. Recounting sum=23: exactly one die is 5, others are 6, so 4 arrangements. Plus sum=24: 1 way. Total = 5/1296. So answer should be 5/1296 = (d).
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