2026-04-22

Problem — 2026-04-22

Easy

Easyprobability

You have an urn with $5$ red and $5$ blue balls. You draw $3$ balls without replacement. What is the probability that all three are the same color?

Express as a fraction

Show solution

Total ways to draw

3

from

10

\binom{10}{3} = 120

. Ways to draw

3

red:

\binom{5}{3} = 10

. Ways to draw

3

blue:

\binom{5}{3} = 10

. So

P(\text{all same color}) = \frac{10 + 10}{120} = \frac{20}{120} = \frac{1}{6}