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nincompoop

  • one year ago

help in dumbing down proof of basic principle of counting.

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  1. danica518
    • one year ago
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    whats the basic principle of counting

  2. danica518
    • one year ago
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    1+1=2 2+1=3 3+1=4

  3. nincompoop
    • one year ago
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    If one experiment can result in any of m possible outcomes and if another experiment can result in any n possible outcomes then there are \(n \times m \rightarrow nm \) possible outcomes of the two experiment.

  4. danica518
    • one year ago
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    if there are n possible outcomes and for each of the n outcomes theres another m that means there has to be n*m

  5. nincompoop
    • one year ago
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    proof ...

  6. danica518
    • one year ago
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    |dw:1437241044215:dw|

  7. danica518
    • one year ago
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    seen in tree diagram

  8. danica518
    • one year ago
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    i think its closely related to understanding the basic ideas of multiplication

  9. danica518
    • one year ago
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    you imagine each outcome of N turning into M outcomes

  10. danica518
    • one year ago
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    so ud have M, N times

  11. nincompoop
    • one year ago
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    \( (1,1), (1,2) ... (1,n)\) \( (2,1), (2,2) ... (2,n)\) \( (m,1), (m,2) ... (m,n)\)

  12. ganeshie8
    • one year ago
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    This amounts to proving the cardinality of cartesian product of two finite sets is same as the product of cardinalities of individual sets : \[n(A\times B) = n(A)\times n(B)\]

  13. ganeshie8
    • one year ago
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    That listing of table will do for proof

  14. ganeshie8
    • one year ago
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    Easy to see that there are m*n entries in that table

  15. nincompoop
    • one year ago
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    and the tree is suppose to help build intuition or some sort

  16. danica518
    • one year ago
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    |dw:1437241650123:dw|

  17. danica518
    • one year ago
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    well to me the tree is pretty much a proof too

  18. nincompoop
    • one year ago
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    I was just doing that last drawing you did

  19. danica518
    • one year ago
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    its saying the same thing, u have n branches and each branch splitting into m parts again

  20. nincompoop
    • one year ago
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    now, let us make it more concrete by providing some real-world example.

  21. danica518
    • one year ago
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    dice is easiest

  22. danica518
    • one year ago
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    1,2,3,5,6 so lets say a kid considers okay all these cases occurred when he threw the dice 1 2 3 4 5 6 now he will be like if i throw the dice again, theres 6 new cases for each of these possiblities 1, 123456 2, 123456 3, 123456 . . 6, 123456

  23. danica518
    • one year ago
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    its like his world split into 6 new worlds,

  24. danica518
    • one year ago
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    LOL

  25. Empty
    • one year ago
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    Flipping a coin and rolling a die. There will be 12 possible outcomes. You can have 1-6 with heads and 1-6 with tails. :P

  26. danica518
    • one year ago
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    |dw:1437242326430:dw|

  27. danica518
    • one year ago
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    in one world the heads was the beginning of all things, and in the other the tail

  28. nincompoop
    • one year ago
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    I think that is when the tree gives a better illustration of what is going on.

  29. anonymous
    • one year ago
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    eh, it usually follows immediately from the definition of multiplication of natural numbers

  30. nincompoop
    • one year ago
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    CORRECT

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