Combinations with Repetition Combinatorics

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How many combinations of k objects can we make from a set of n objects when we allow for reptition? We'll go over an interesting solution to this question in today's combinatorics lesson. We consider a number of spaces in which we can place n-1 bars to completely describe a combination with repetition. Furthermore every possible combination with repetition can be described by a placement of bars, and so we reduce the problem to a normal combination problem, counting how many ways we can place bars in spaces! • The combination formula and why it works: • The Combination Formula and Why it Wo... • Permutations with repetition: • Permutations with Repetition | Combin... • Number of 4-Digit Codes with and without Repetition: • Number of 4-Digit Codes With and With... • Symmetric property of binomial coefficients: • Symmetric Property of Binomial Coeffi... • Thanks to Nasser Alhouti, Robert Rennie, Barbara Sharrock, and Lyndon for their generous support on Patreon! • ◆ Donate on PayPal: https://www.paypal.me/wrathofmath • ◆ Support Wrath of Math on Patreon: / wrathofmathlessons • I hope you find this video helpful, and be sure to ask any questions down in the comments! • +WRATH OF MATH+ • Follow Wrath of Math on... • ● Instagram: / wrathofmathedu • ● Facebook: / wrathofmath • ● Twitter: / wrathofmathedu • My Music Channel: / @emery3050

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