Stars and bars (combinatorics)

In combinatorics, stars and bars (also called "sticks and stones",[1] "balls and bars",[2] and "dots and dividers"[3]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve many simple counting problems, such as how many ways there are to put n indistinguishable balls into k distinguishable bins.[4]

Theorems one and two are the coefficients used for 2 different support ranges in the negative binomial probability distribution.

  1. ^ Batterson, J. Competition Math for Middle School. Art of Problem Solving.
  2. ^ Flajolet, Philippe; Sedgewick, Robert (June 26, 2009). Analytic Combinatorics. Cambridge University Press. ISBN 978-0-521-89806-5.
  3. ^ "Art of Problem Solving". artofproblemsolving.com. Retrieved 2021-10-26.
  4. ^ Feller, William (1968). An Introduction to Probability Theory and Its Applications. Vol. 1 (3rd ed.). Wiley. p. 38.