Saved on this device

Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

The Multinomial Theorem and Enumerating Outcomes with Repetition

Quick fact

The multinomial coefficient (n; k₁, k₂, …, kₘ) = n! / (k₁! k₂! … kₘ!) counts the number of distinct permutations of n objects where there are k₁ identical items of type 1, k₂ of type 2, and so on, and this same number appears as the coefficient in the expansion of (x₁ + x₂ + … + xₘ)ⁿ.

Why this is interesting

You know how to expand (a+b)², but what happens when you have (a+b+c)³? How many different terms appear, and how do you know their coefficients without multiplying everything out?