Visualizing combinations with repetitions allowed.

Asked Jun 04 '18 at 13:00

Active Jun 05 '18 at 09:45

Viewed 438 times

So I fully understand:

Permutations without repetitions: $\dfrac {n!}{(n-r)!}$

Permutations with repetitions: $n^r$

Combinations without repetitions: $\dfrac{n!}{(n-r)!r!}$

But I'm having problems finding resources online that visually explain combinations with repetitions: $$\dfrac{(n+r-1)!}{(n-1)!r!}$$

I would be very grateful if anyone could give me a good visual, step by step explanation of how they work. Maybe use the case of choosing $3$ letters from a set of A, B and C, with repetitions allowed.

edited Jun 05 '18 at 09:45

asked Jun 04 '18 at 13:00

mbkoverflow

Possible duplicate? https://math.stackexchange.com/questions/208377/combination-with-repetitions – Tony Hellmuth Jun 04 '18 at 13:16
Hmmm. But I how can it applied to a case such as the one I mentioned with the letters A, B and C? – mbkoverflow Jun 04 '18 at 13:47
For that, you might want to check out the examples here: http://www.math.northwestern.edu/~mlerma/courses/cs310-05s/notes/dm-gcomb :) – Tony Hellmuth Jun 04 '18 at 13:51
Also there are a few very similar examples here on Math Exchange, just check out the "Related" tabs :) – Tony Hellmuth Jun 04 '18 at 13:58
Wait but why does the 18 upvotes answer have $k-1$ at the bottom of the binomial instead of $k$? – mbkoverflow Jun 05 '18 at 09:44

Visualizing combinations with repetitions allowed.

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