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Solve the equation ^nP3 = 24 ^nC4 for n.

Mathematics

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Step-by-step solution

3 steps

  1. Write the formulas for permutations and combinations.

    The formula for nPr^nP_r is nPr=n!(n−r)!^nP_r = \frac{n!}{(n-r)!}.
    The formula for nCr^nC_r is nCr=n!r!(n−r)!^nC_r = \frac{n!}{r!(n-r)!}.

  2. Apply the formulas to the given equation.

    The given equation is nP3=24nC4^nP_3 = 24nC_4.
    Substitute the formulas:

    n!(n−3)!=24×n!4!(n−4)!\frac{n!}{(n-3)!} = 24 \times \frac{n!}{4!(n-4)!}

  3. Simplify the equation.

    For the terms to be defined, we must have $n \

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