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- #2

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There are well over 800 possibilities.

- #3

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How much is well over 800? And how do you figure that out?There are well over 800 possibilities.

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- #5

Integral

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http://en.wikipedia.org/wiki/Combinatorics" [Broken] has the answer. In this case, order does not matter and and you can order the same thing more then once. (2 Arby sandwichs and 3 frys)

edit: I get 792

edit: I get 792

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- #6

cristo

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The answer is not "way more than 790," but is actually 792. Check the "combination with repetition" section of this page of wikipedia.

- #7

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All selections are independant, but 8^5 doesn't take into account any duplications of choices this is what I thought at first as well and realized it made no sense.

- #8

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Oops, sorry, I just realized.

- #9

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Say I have 3 items A,B,C and I wish to select 3 at a time (order does not matter and an object can be chosen more than once)...

using the forumla for Combination with repetition, I should have (3+3-1)!/3!*2!=10 combinations

If I list all the possible combinations, I have:

AAA BBB CCC

AAB BBC

AAC BCC

ABB

ACC

But this is only 9.....what combination am I missing?

- #10

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sorry.. didn't look at the most obvious choice.. ABC!!!

- #11

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i was curious as to why they said over 790 choices, as that would seem to imply it's between 790 and 800 (or else they would have said over 800 choices).

there are 8 choices, and 5 slots to put them in. that should be 8^5 if i remember from discrete math. 8^5 is a lot larger than 790 though.

- #12

cristo

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Read post #5 or #6.there are 8 choices, and 5 slots to put them in. that should be 8^5 if i remember from discrete math. 8^5 is a lot larger than 790 though.

- #13

cepheid

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Er, yeah, because the order of the elements doesn't matter. You're just choosing, not permuting. If you order two medium drinks, two curly fries and a roast beef sandwich, that's the same as ordering a roast beef sandwich, an order of curly fries, a medium drink, another order of curly fries, and a medium drink. You've put in the same food order, you just haven't requested the items in the same sequence. The two examples are not distinct combinations of five items.there are 8 choices, and 5 slots to put them in. that should be 8^5 if i remember from discrete math. 8^5 is a lot larger than 790 though.

What Cristo said, if you want to see the mathematics.

By the way, here in Canada, you still pay $6, but you only get to choose four items! I don't understand why that is. The menu says 330 possible combinations, which leads me to believe that there are still 8 items to choose from (if you use the formula provided in the Wikipedia link, it works out exactly).

That leads me to my next question. Does anyone know how to "derive" or at least intuitively explain this formula for combination with repetition? Because, all three of the other combinatorial formulas make perfect sense to me (and if you don't believe me, I'd be happy to explain why I think they make sense intuitively). But combination with repetitition...looking at the formula, I can't seem to figure out how one might arrive at it.

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