Combinations with Repetition | Combinatorics

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: https://www.youtube.com/watch?v=wKgiSUnbLxE Permutations with repetition: https://www.youtube.com/watch?v=DwQa6kfMIgc Number of 4-Digit Codes with and without Repetition: https://www.youtube.com/watch?v=Khgg-mJUB-0 Symmetric property of binomial coefficients: https://www.youtube.com/watch?v=pbKmRumnmjM 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: https://www.patreon.com/join/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: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Music Channel: https://www.youtube.com/channel/UCOvWZ_dg_ztMt3C7Qx3NKOQ