Multinomial Coefficients

Probability · Axiom Academy

LESSON Multinomial Coefficients Extending combinations to multiple groups 1. From Binomial to Multinomial The binomial coefficient C(n,r) divides n items into 2 groups: r chosen items and (n-r) unchosen items. Multinomial coefficients divide n items into 3 or more groups. To divide n items into k groups of sizes n₁, n₂, ..., nₖ (where n₁ + n₂ + ... + nₖ = n), use the multinomial coefficient. Let's see how this formula works: 3. Worked Example: Distributing Tasks You have 10 tasks to distribute: 4 to Alice, 3 to Bob, and 3 to Carol. How many ways can you assign the tasks? 4. Application: Anagrams with Repetition A classic application: How many distinct arrangements exist for the letters in "MISSISSIPPI"?

This is the written version of the interactive lesson above. See the full Probability course.