Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 480

\[1)\ C_{13}^{10} + C_{13}^{11} = C_{13}^{10} + C_{13}^{10 + 1} =\]

\[= C_{13 + 1}^{10 + 1} = C_{14}^{11} = \frac{14!}{11!(14 - 11)!} =\]

\[= \frac{14 \bullet 13 \bullet 12 \bullet 11!}{11! \bullet 3!} =\]

\[= \frac{14 \bullet 13 \bullet 12}{3 \bullet 2} = 364.\]

\[2)\ C_{14}^{3} + C_{14}^{2} = C_{14}^{2} + C_{14}^{2 + 1} =\]

\[= C_{14 + 1}^{2 + 1} = C_{15}^{3} = \frac{15!}{3!(15 - 3)!} =\]

\[= \frac{15 \bullet 14 \bullet 13 \bullet 12!}{3! \bullet 12!} =\]

\[= \frac{15 \bullet 14 \bullet 13}{3 \bullet 2} = 455.\]