2026-03-25

Problem — 2026-03-25

Medium

Mediumprobability

You roll a fair six-sided die $3$ times. What is the probability that the three results are in strictly increasing order?

Express as a fraction

Show solution

We need three distinct values arranged in increasing order. There are

\binom{6}{3} = 20

ways to choose the three values, and each set has exactly one increasing arrangement. The total outcomes are

6^3 = 216

. So the probability is

\frac{20}{216} = \frac{5}{54}