Math Question!

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Math Question!

by michscan @ 2008-06-20 – 16:24:21

how many different seven number combinations could you get from seventeen numbers?
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11 Comments to Math Question!

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- Jenniebaby
- 2008-06-20 @ 16:35:01
Depends whether your combinations are ordered or not - ie is 1234567 the same as 7654321?
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- michscan
- 2008-06-20 @ 16:51:54
These are the 18 numbers that i would like to know how many 7 numbner combinations could be had:

5, 7, 11, 12, 14, 19, 22, 23, 24, 25, 27, 29, 32, 34, 36, 39, 40, 41
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- Jenniebaby
- 2008-06-20 @ 17:11:58
If you allow permutations (ie if 1234567 is different from 7654321) then there are 160,392,960 possible permutations.

However, if you disallow them (so that 1234567 is the same as 7654321) there are only 31,824.
- - michscan
  - 2008-06-20 @ 17:15:07
  Thanks, that is huge... tell me though how did you arrive at that number? what is the formula to use?
  - - Jenniebaby
    - 2008-06-20 @ 17:24:25
    For permutations we write 17_P_7 which is defined (and calculated) as follows:
    
    17_P_7 = 17!/(17-7)! = 17!/10!
    =(17*16*15*...*2*1)/(10*9*...*2*1)
    = 17*16*15*...*11
    = 98,017,920
    
    For no permutations, we write 17_C_7 (say '17 choose 7'), where:
    
    17_C_7 = (17_P_7)/7!
    = (17*16*...*2*1)/(7*6*...*2*1)
    = 98,017,920/5,040
    = 19,448
    
    See?
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- Jenniebaby
- 2008-06-20 @ 17:16:17
Oops - sorry - I did it from 18 numbers, not 17.

For 17, answers are 98,017,920 if permutations are allowed and 19,448 if not.
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- grumpus ^Pro
- http://bobmblack.blog.co.uk
- 2008-06-20 @ 18:31:16
Next question ... what practical purpose (if any) does this specific question actually serve?
I'm truly interested.
?Gambling of some sort?
- - grumpus ^Pro
  - http://bobmblack.blog.co.uk
  - 2008-06-21 @ 16:47:17
  Thought it was something like that. Sounds like a big investment to be sure of winning. Good luck! And don't lose all those tickets!
  - - michscan
    - 2008-06-21 @ 18:48:59
    thanks, won't be spending that amount to play...
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- michscan
- 2008-06-21 @ 00:14:43
yes, it is for one of our lotteries here in Canada called Lotto Super 7; where you have to pick 7 out of 47 numbers to try and win...
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- trintrin1x
- 2008-06-24 @ 15:19:21
Totally baffled? x
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