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I've been wondering whether there's an intuitive way to understanding combinations with repetition, so that you would just use the basic rules of the sum and product instead of going with the handy formula that pertains to said combinations.

I had an example where in a flowershop you have 4 different kinds of flowers. You want to make bouquets of 7 flowers, and the question is how many different kinds of bouquets you can thus make. Now if you plug everything in the (n+k-1 k) it's all good and you get the result, but I just can't get my head around how you'd do that without using the said equation. Or if you use it, how do you make intuitive sense of it? I guess what I'm asking is is whether there's something akin to the connection between the rule of product and permutations where, for example, if you have to set up 4 different kinds of flowers into a bouquet of 4 flowers where order plays a role you can pretty much see where the 4! equation comes from, as you can just as easily write down 4 (options for the first flower), 3 (options for the second flower), 2 (-||-) and 1.

Now I've read the example on wikipedia, but I didn't find it to help me understand why you're plugging in those numbers on an intuitive level, it just helps in understanding why you use the above-mentioned formula.

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# Combinations with repetition (an intuitive way to it?)

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