When six unbiased dice are rolled simultaneously, the probability of getting…

2024

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

  1. A.

    1/324

  2. B.

    5/324

  3. C.

    7/324

  4. D.

    11/324

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Show answer & explanation

Correct answer: B

Solution: Compute the number of favorable and total outcomes.

  1. Total outcomes = 6^6 = 46,656.

  2. Favorable outcomes = number of ways to get all six different faces = permutations of 1–6 = 6! = 720.

  3. Probability = 6! / 6^6 = 720 / 46,656 = 5 / 324.

  4. Alternate view (sequential multiplication): (6/6)·(5/6)·(4/6)·(3/6)·(2/6)·(1/6) = 720 / 46,656 = 5 / 324.

Answer: 5/324.

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