Question

Use a calculator to evaluate 30 C1130 C11(Simplify your answer. Type an integer or a fraction.)

Answer 1

30C11 refers to:

$30C11=\frac{30!}{11!(30-11)!}$

Then,

$\begin{gathered} 30C11=\frac{30!}{11!(30-11)!} \\ =\frac{30!}{11!\cdot19!}=\frac{30\cdot29\cdot28\cdot27\cdot26\cdot25\cdot24\cdot23\cdot22\cdot21\cdot20}{11!} \\ =64627300 \end{gathered}$

Remember that, if n is a natural number:

$n!=1\cdot2\cdot3\cdot\ldots\cdot n$

Therefore, the answer is 54627300