GMAT Quantitative · Question of the Day

GMAT Quantitative Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.

Saturday, September 5, 2026

A box contains 10 balls: 4 red, 3 green, and 3 yellow. If 3 balls are drawn simultaneously, what is the probability that no two balls have the same color?

Keep practicing GMAT Quantitative

Question of the Day

Answer today's GMAT Quantitative question, reveal the full explanation, then keep the streak going with a new question every day.

A box contains 10 balls: 4 red, 3 green, and 3 yellow. If 3 balls are drawn simultaneously, what is the probability that no two balls have the same color?

$\frac{3}{10}$ (correct answer)
$\frac{36}{120}$
$\frac{1}{3}$
$\frac{2}{5}$

Explanation: For no two balls to have the same color, we need exactly one ball of each color. Ways to choose 1 red from 4: C(4,1) = 4. Ways to choose 1 green from 3: C(3,1) = 3. Ways to choose 1 yellow from 3: C(3,1) = 3. Total favorable outcomes = 4 × 3 × 3 = 36. Total ways to choose 3 balls from 10: C(10,3) = 120. Probability = 36/120 = 3/10. Choice B shows the unreduced fraction 36/120. Choice C (1/3) would result from 40/120. Choice D (2/5) would result from 48/120. The correct answer is A.