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GATE 2024 CS (CS2) – Question 18

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

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. $\frac{1}{324}$
  2. $\frac{5}{324}$
  3. $\frac{7}{324}$
  4. $\frac{11}{324}$

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Show answer and explanation

Correct answer: (B) $\frac{5}{324}$

Explanation

Favourable outcomes = 6! = 720 out of 6^6 = 46656. Probability = 720/46656 = 5/324.