Probability & Combinatorics
Advanced

Stars and Bars

Ways to distribute n identical items into k distinct groups.

Formula

(n+k−1k−1)\binom{n+k-1}{k-1}

Variables

nItems
kGroups

Example

5 candies to 3 kids: C(7,2) = 21

Did You Know?

A classic technique for counting non-negative integer solutions.

countingcombinatorics