QuestionQuestion 26: If ${ }^{n} P_{3}=4^{n} C_{5}$, then $n$ equals
Single-digit integer (-9 to 9)
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Studdy Solution
Factor the quadratic equation:
$$(n - 9)(n + 2) = 0$$
Set each factor to zero and solve for $n$:
$$n - 9 = 0 \quad \Rightarrow \quad n = 9$$
$$n + 2 = 0 \quad \Rightarrow \quad n = -2$$
Since $n$ must be a positive integer (as it represents a count of items), we choose:
$$n = 9$$
The value of $n$ is:
$$\boxed{9}$$