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mathmath333

  • one year ago

counting question

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{How many different sums can be formed by the following }\ ?\hspace{.33em}\\~\\ & \normalsize 5\ \text{dollar},\ 1\ \text{dollar},\ 50\ \text{cents},\ 25\ \text{cents},\ 10\ \text{cents},\ 3\ \text{cents},\ 2\ \text{cents},\ 1\ \text{cent.} \hspace{.33em}\\~\\ \end{align}}\)

  2. welshfella
    • one year ago
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    I guess if you take 2 at a time its 8C2 right?

  3. welshfella
    • one year ago
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    the 3 at a time it will be 8C3

  4. mathmath333
    • one year ago
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    yes u can also take 3 ,4, 5 upto 8 at a time

  5. welshfella
    • one year ago
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    yes - but could there be any duplicates in all these?

  6. mathmath333
    • one year ago
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    just need to deduct the double count like example 2 cent and 1 cent taken both are equal to 3 cent taken once

  7. welshfella
    • one year ago
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    yes exactly

  8. mathmath333
    • one year ago
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    ^duplication

  9. welshfella
    • one year ago
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    and of course there is 8C1 singles

  10. mathmath333
    • one year ago
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    yes

  11. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \dbinom{8}{1}+\dbinom{8}{2}+\cdots+\dbinom{8}{8}=2^{8}-1 \hspace{.33em}\\~\\ \end{align}}\)

  12. welshfella
    • one year ago
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    i think the only duplicates are the ones you mentioned

  13. mathmath333
    • one year ago
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    yes but consider 5 dollar +1cent +2 cent =5 dollar+3cent

  14. mathmath333
    • one year ago
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    this also duplication

  15. welshfella
    • one year ago
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    right

  16. welshfella
    • one year ago
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    and 1 dollar + 3 , 1 dollar + 1 + 2

  17. mathmath333
    • one year ago
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    yes all are considered

  18. welshfella
    • one year ago
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    - also same for 50 , 25, 10 cents

  19. mathmath333
    • one year ago
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    yep

  20. welshfella
    • one year ago
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    only combinations we are concerned with here right? not permutations

  21. welshfella
    • one year ago
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    - yes - bacuase we are dealing with sums only

  22. mathmath333
    • one year ago
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    yes only addition (result) is counted

  23. welshfella
    • one year ago
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    that identity, = 2^8 - 1 I haven't seen that before.

  24. mathmath333
    • one year ago
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    google sum of combinations u will get it

  25. mathmath333
    • one year ago
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    https://www.physicsforums.com/threads/sum-of-combinations.83309/

  26. welshfella
    • one year ago
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    right so how do we go about counting the number of duplicates?

  27. mathmath333
    • one year ago
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    yea i m confused about that the main thing

  28. triciaal
    • one year ago
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    @phi

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