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anonymous

  • one year ago

Simplfy (n) - (n-1) (r) (r)

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  1. anonymous
    • one year ago
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    \[\left(\begin{matrix}n \\ r\end{matrix}\right) - \left(\begin{matrix}n-1 \\ r\end{matrix}\right)\]

  2. anonymous
    • one year ago
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    simplify

  3. welshfella
    • one year ago
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    |dw:1443370171228:dw|

  4. welshfella
    • one year ago
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    I'm feeling my way here ... and i'm not sure if it will lead to much simplification...

  5. welshfella
    • one year ago
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    oh i misread the question the second part is |dw:1443371547831:dw|

  6. anonymous
    • one year ago
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    yea

  7. welshfella
    • one year ago
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    well i've got an expression which contains factorials but its not that simple!

  8. welshfella
    • one year ago
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    |dw:1443372120105:dw|

  9. anonymous
    • one year ago
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    \[\begin{align*}\binom nr-\binom{n-1}r&=\frac{n!}{r!(n-r)!}-\frac{(n-1)!}{r!(n-1-r)!}\\[1ex] &=\frac{(n-1)!}{r!(n-1-r)!}\left(\frac{n}{(n-r)}-1\right)\\[1ex] &=\frac{(n-1)!}{r!(n-1-r)!}\left(\frac{n-(n-r)}{(n-r)}\right)\\[1ex] &\vdots \end{align*}\]

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spraguer (Moderator)
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