Подставляя в формулу

\(\displaystyle C_\color{orange}{n}^{\color{violet}{k}}=\frac{\color{orange}{n}!}{\color{violet}{k}!(\color{orange}{n}-\color{violet}{k})!}\) 

\(\displaystyle \color{orange}{n}=\color{orange}{6}\) и \(\displaystyle \color{violet}{k}=\color{violet}{2} \small, \)получаем:

\(\displaystyle C_\color{orange}{6}^{\color{violet}{2}}=\frac{\color{orange}{6}!}{\color{violet}{2}!(\color{orange}{6}-\color{violet}{2})!}=\frac{6!}{2! \cdot 4!}=\frac{5 \cdot 6 }{2}=\color{green}{15} \small.\)

Подставляя в формулу

\(\displaystyle C_\color{orange}{n}^{\color{violet}{k}}=\frac{\color{orange}{n}!}{\color{violet}{k}!(\color{orange}{n}-\color{violet}{k})!}\) 

\(\displaystyle \color{orange}{n}=\color{orange}{6}\) и \(\displaystyle \color{violet}{k}=\color{violet}{3} \small, \)получаем:

\(\displaystyle C_\color{orange}{6}^{\color{violet}{3}}=\frac{\color{orange}{6}!}{\color{violet}{3}!(\color{orange}{6}-\color{violet}{3})!}=\frac{6!}{3! \cdot 3!}=\frac{4 \cdot 5 \cdot 6 }{1 \cdot 2 \cdot 3}=\color{blue}{20} \small.\)

Подставляя в формулу

\(\displaystyle C_\color{orange}{n}^{\color{violet}{k}}=\frac{\color{orange}{n}!}{\color{violet}{k}!(\color{orange}{n}-\color{violet}{k})!}\) 

\(\displaystyle \color{orange}{n}=\color{orange}{7}\) и \(\displaystyle \color{violet}{k}=\color{violet}{3} \small, \)получаем:

\(\displaystyle C_\color{orange}{7}^{\color{violet}{3}}=\frac{\color{orange}{7}!}{\color{violet}{3}!(\color{orange}{7}-\color{violet}{3})!}=\frac{7!}{3! \cdot 4!}=\frac{5 \cdot 6\cdot 7 }{1 \cdot 2 \cdot 3}=\color{red}{35} \small.\)