MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Token Distribution Color Constraint Probability

1675AdeptCombinatoricsProbability

AMC 12 A

A set of 12 tokens—3 red, 2 white, 1 blue, and 6 black—is to be distributed at random to 3 game players, 4 tokens per player. The probability that some player gets all the red tokens, another player gets all the white tokens, and the remaining player gets the blue token can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m + n$? (A) 387 (B) 388 (C) 389 (D) 390 (E) 391
0 students attempted0% solvedRating 1675

Related practice paths

AIME PracticeInteger-answer practice for deeper multi-step problems.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.