Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 472

\[= \frac{6 \bullet 5 \bullet 4!}{3! \bullet 4!} + \frac{11 \bullet 10 \bullet 9 \bullet 8 \bullet 7 \bullet 6!}{5! \bullet 11 \bullet 6!} =\]

\[= \frac{6 \bullet 5}{3 \bullet 2} + \frac{10 \bullet 9 \bullet 8 \bullet 7}{5 \bullet 4 \bullet 3 \bullet 2} =\]

\[= 5 + 3 \bullet 2 \bullet 7 = 5 + 42 = 47.\]

\[2)\ \left( \frac{C_{11}^{7}}{10} - \frac{C_{7}^{2}}{7} \right) \bullet \frac{P_{5}}{A_{6}^{4}} =\]

\[= \left( \frac{11 \bullet 9 \bullet 8}{4 \bullet 3 \bullet 2} - \frac{6}{2} \right) \bullet \frac{5! \bullet 2}{6 \bullet 5!} =\]

\[= (11 \bullet 3 - 3) \bullet \frac{1}{3} = 11 - 1 = 10.\]