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Math Help - combination equation

  1. #1
    Super Member dhiab's Avatar
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    combination equation

    Solve in R :
    n , p naturels numbers and
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Observe that

    ^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\ =\ ^n\mathrm C_p

    Hence

    x^2\,-\,^n\mathrm C_px\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p


    =\ x^2\,-\,\left(^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\right)x\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p


    =\ \left(x\,-\,^{n-1}\mathrm C_{p-1}\right)\left(x\,-\,^{n-1}\mathrm C_p\right)
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by TheAbstractionist View Post
    Observe that
    ^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\ =\ ^n\mathrm C_p
    Hence
    x^2\,-\,^n\mathrm C_px\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p
    =\ x^2\,-\,\left(^{n-1}\mathrm C_{p-1}\,+\,^{n-1}\mathrm C_p\right)x\,+\,^{n-1}\mathrm C_{p-1}\cdot^{n-1}\mathrm C_p


    =\ \left(x\,-\,^{n-1}\mathrm C_{p-1}\right)\left(x\,-\,^{n-1}\mathrm C_p\right)
    Hello : Thank you
    it is necessary to discuss the number of resolution according to paramétres n , p
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