Compute .

$$\boxed{ \small{\text{$\left( \begin{array}{c}n \\k\end{array} \right) =\dfrac{n!}{k!\cdot (n-k)!} $}} }$$

$$\small{\text{$\left( \begin{array}{c}223 \\ 221 \end{array} \right)=\dfrac{223!}{221!\cdot (223-221)!}= \dfrac{\not{221!} \cdot 222 \cdot 223 }{\not{221!}\cdot 2!}= \dfrac{222 \cdot 223 }{2}= 111\cdot 223 = 24753$}}$$