2026-04-13

Problem — 2026-04-13

Easy

Easyprobability

You roll $5$ fair six-sided dice. What is the probability that at least two dice show the same number?

Express as a fraction

Show solution

Use the complement.

P(\text{all different}) = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2}{6^5} = \frac{720}{7776} = \frac{5}{54}

. So

P(\text{at least two same}) = 1 - \frac{5}{54} = \frac{49}{54}