GATE CSE 2024 Session 2 Q18: Probability six dice show all different numbers

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

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Answer: B (official GATE 2024 final answer key)

Concept used: Favourable outcomes are the permutations of 1–6 among $6^6$ equally likely outcomes.

First step: Probability $= \dfrac{6!}{6^6} = \dfrac{720}{46656}$ ; simplify.

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Source: official GATE 2024 Session 2 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key