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    • ▾Combinatorics
      • •Stirling numbers
      • ▸Catalan numbers
        • •Counting Binary Ops (NRICH activity)
        • •Number of ways to triangulate a regular polygon
        • ▸Young tableau
          • •One Basket or Group Photo (NRICH activity)
      • •Combinatorial proof: Binomial theorem
      • •Double counting
      • •History of combinatorics
      • •Inclusion–exclusion principle
      • ▸Pigeonhole principle
        • •Picking socks in the dark
      • •Proving Vandermonde's identity
      • •Stars and bars
      • •Sum and product rules
      • •Sum of squares of binomial coefficients
      • •Bell numbers
     › Combinatorics

    Stars and bars

    How many ways can you split 11 identical coins to 3 people? How many ways if each person has to get at least 1 coin?
    72598How To Solve A TOUGH Interview Question - Ways To Give 11 Coins To 3 People
    MindYourDecisions
    2019 AMC 8/Problem 25 Alice has \(24\) apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?
    7979Solution 1 - 2019 AMC 8 Problems/Problem 25
    AoPS Online

    YouTube videos

    • 508Stars and Bars (and bagels) - Numberphile
      Numberphile
    • 69870Stars and Bars Counting – Introduction to Mathematical Thinking
      Introduction to Mathematical Thinking
    • 69871Addition, Stars, and Bars
      Michael Barrus
    • 69872Stars and Bars Questions | Permutations and Combinations
      Magnus Prep
    • 69876AMC10/12 Prep: Ball and Urn Counting
      Walt S

    Textbook sections

    • 16Section 1.5: Stars and Bars
      Discrete Mathematics: An Open Introduction