# Test: Binomial Series - Ambitious

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Question 1:   Find the value of $\frac{16!}{13!}$
$\frac{16}{13}$
$0$
$3360$
$240$
Question 2:   Find the value of $\frac{4!}{0!}$
Does not exist
$1$
$0$
$24$
Question 3:   Knowing that combinational coefficient ${C}_{r}^{n}=\frac{n!}{\left(n-r\right)r!}$, find ${C}_{1}^{5}$
$25$
$5$
$0$
$1$
Question 4:   Simplify: $\frac{\left(3n\right)!}{\left(3n+2\right)!}$
$\frac{3n}{3n+2}$
$\frac{1}{{\left(3n+3\right)}^{2}}$
$\frac{1}{\left(3n+3\right)\left(3n+2\right)}$
$\frac{1}{\left(3n+2\right)\left(3n+1\right)}$
Question 5:   Find the coefficient of ${x}^{4}$in the binomial expansion of ${\left(2-\frac{3}{x}\right)}^{9}$
$\frac{353682}{{x}^{4}}$
$\frac{326592}{{x}^{4}}$
$\frac{1}{{x}^{4}}$
$\frac{647378}{{x}^{4}}$
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