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Subject: Quick Math Question rss

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Carl Garber
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So, I am not that greatest at math and was hoping someone here could help me out. I am designing a game with 6 resources and I am wondering how many different combinations of 3 can be made with them. resources can be more than one of the three spots(ie. red, red, green). But position doesn't matter(ie. red, red, green and red, green, red are the same). This is a pricing system and I am just trying to determine whether I can use all possible combinations in my game, whether I will need doubles of some, or whether I will just have to use a portion of the combinations available.

Thanks!
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Martin Windischer
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n: number of resources
k: how many you choose

combination with repetition: (n+k-1) choose (k), which gives (8 choose 3)=56
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Carl Garber
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thanks for that quick response! I think that'll work for my game quite well
 
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Rich Shipley
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6 all the same color

30 (6*5) two of one color and one of another

20 (6*5*4/6) three unique colors in any order

So 56 total.
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DigitalMan
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Here's a good site for this sort of thing... it even produced this listing for me:

http://www.mathsisfun.com/combinatorics/combinations-permuta...

Quote:
Combinations with repetition (n=6, r=3)

List has 56 entries.

{gold,gold,gold} {gold,gold,ore} {gold,gold,steel} {gold,gold,wood} {gold,gold,beer} {gold,gold,sheep} {gold,ore,ore} {gold,ore,steel} {gold,ore,wood} {gold,ore,beer} {gold,ore,sheep} {gold,steel,steel} {gold,steel,wood} {gold,steel,beer} {gold,steel,sheep} {gold,wood,wood} {gold,wood,beer} {gold,wood,sheep} {gold,beer,beer} {gold,beer,sheep} {gold,sheep,sheep} {ore,ore,ore} {ore,ore,steel} {ore,ore,wood} {ore,ore,beer} {ore,ore,sheep} {ore,steel,steel} {ore,steel,wood} {ore,steel,beer} {ore,steel,sheep} {ore,wood,wood} {ore,wood,beer} {ore,wood,sheep} {ore,beer,beer} {ore,beer,sheep} {ore,sheep,sheep} {steel,steel,steel} {steel,steel,wood} {steel,steel,beer} {steel,steel,sheep} {steel,wood,wood} {steel,wood,beer} {steel,wood,sheep} {steel,beer,beer} {steel,beer,sheep} {steel,sheep,sheep} {wood,wood,wood} {wood,wood,beer} {wood,wood,sheep} {wood,beer,beer} {wood,beer,sheep} {wood,sheep,sheep} {beer,beer,beer} {beer,beer,sheep} {beer,sheep,sheep} {sheep,sheep,sheep}
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