^np_x=n!/(n x)! ^np_4=20× ^np_2 (n)×(n 1)×(n 2)×(n 3)=5× 4×(n)×(n 1) (n 2)×(n 3)=5×4 n=7 ...

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Linear Equation in One Variable

np4=20 ×np2 f...

Question

$^{n} p_{4} = 20 \times^{n} p_{2}$ find $n$

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Solution

$^{n} p_{x} = \frac{n!}{(n - x)!}$
$^{n} p_{4} = 20 \times^{n} p_{2}$
$(n) \times (n - 1) \times (n - 2) \times (n - 3) = 5 \times 4 \times (n) \times (n - 1)$
$(n - 2) \times (n - 3) = 5 \times 4$
$n = 7$

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