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NDA 2026 · PYQ · Probability / Dice · medium

Four dice are rolled. What is the probability that getting a total of the numbers on the dice is 6?

  1. A.1/216
  2. B.1/324
  3. C.5/648✓ Correct
  4. D.7/648

Explanation

Number of ways to get sum 6 with four dice (each ≥ 1): number of solutions to a+b+c+d = 6 with 1 ≤ each ≤ 6. Substituting a' = a-1 etc., a'+b'+c'+d' = 2 with each ≥ 0: C(5,3) = 10 ways. Total outcomes = 6⁴ = 1296. Probability = 10/1296 = 5/648.
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