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:    • 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...  

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