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I am trying to understand what permutations mean, so I am taking two 6 sided dice and rolling, the total permutations are 36 - this is something that I understand

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

now I want to understand the permutation formula nPr=n!(n−r)! for the same use case above

  • what is n and what is r? if n=6 and r=2 then the number of permutations only come to 30 and not 36, so my n and r are not correct.
hp 5g
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    Your two dice demonstrate the multiplication principle. This is not an example of permutations. – Karl Apr 14 '23 at 22:10
  • When both dice come out the same, maybe it doesn't count? – herb steinberg Apr 14 '23 at 22:14
  • Permutations with $n=6,r=2$ mean that you are considering the ways of choosing $2$ (diferent) things out of $6$. You can't consider $(6,6)$ and $(4,4)$ a valid permutation. Then, if you subctract 6 from 36 you get 30. – RicardoMM Apr 14 '23 at 22:28
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    For example, how many ways are there for 5 friends to seat in 2 seats? The answer is $5P2$. You can't have the same person sit in the 2 seats at once! – RicardoMM Apr 14 '23 at 22:29
  • @Karl thanks a lot for the links and I think I am getting some understanding. Not sure if this question makes sense but how can I apply this permutations concept for - permutations of two dice taken two at a time – hp 5g Apr 15 '23 at 01:59
  • Permutations arise when repeated values can't occur in the outcomes you're counting. When rolling multiple dice, you can get the same value on two or more of them, so permutation's aren't directly applicable. Also, I don't know what you mean by "two dice taken two at a time". Can you give an example of one of the outcomes you're trying to count? – Karl Apr 15 '23 at 02:15
  • @Karl thanks again, I am slowly getting it but I think I am mixing up the multiplication principle with permutations big time, when I roll 2 dice one of the outcome could be {1,2} and when I count all the permutations there will be 36. I was trying to make a connection between this manual process of counting and calculating permutations using the nPr formula. I re-read the links you mentioned and I don't think I am correct in doing that. – hp 5g Apr 15 '23 at 03:20

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