Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 445

\[1)\ C_{6}^{2} = \frac{6!}{2!(6 - 2)!} = \frac{6 \bullet 5 \bullet 4!}{2 \bullet 4!} =\]

\[= 3 \bullet 5 = 15;\]

\[2)\ C_{8}^{3} = \frac{8!}{3!(8 - 3)!} = \frac{8 \bullet 7 \bullet 6 \bullet 5!}{3 \bullet 2 \bullet 5!} =\]

\[= 8 \bullet 7 = 56;\]

\[3)\ C_{8}^{6} = \frac{8!}{6!(8 - 6)!} = \frac{8 \bullet 7 \bullet 6!}{6! \bullet 2!} =\]

\[= \frac{8 \bullet 7}{2} = 4 \bullet 7 = 28;\]

\[4)\ C_{8}^{5} = \frac{8!}{5!(8 - 5)!} = \frac{8 \bullet 7 \bullet 6 \bullet 5!}{5! \bullet 3!} =\]

\[= \frac{8 \bullet 7 \bullet 6}{3 \bullet 2} = 8 \bullet 7 = 56;\]

\[5)\ C_{9}^{1} = \frac{9!}{1!(9 - 1)!} = \frac{9 \bullet 8!}{1 \bullet 8!} = 9;\]

\[6)\ C_{9}^{8} = \frac{9!}{8!(9 - 8)!} = \frac{9 \bullet 8!}{8! \bullet 1!} = 9;\]

\[7)\ C_{10}^{10} = \frac{10!}{10!(10 - 10)!} = \frac{1}{0!} =\]

\[= \frac{1}{1} = 1;\]

\[8)\ C_{10}^{0} = \frac{10!}{0!(10 - 0)!} = \frac{10!}{1 \bullet 10!} =\]

\[= \frac{1}{1} = 1;\]

\[9)\ C_{10}^{3} = \frac{10!}{3!(10 - 3)!} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7!}{3 \bullet 2 \bullet 7!} = 5 \bullet 3 \bullet 8 = 120;\]

\[10)\ C_{10}^{7} = \frac{10!}{7!(10 - 7)!} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7!}{7! \bullet 3!} = \frac{10 \bullet 9 \bullet 8}{3 \bullet 2} =\]

\[= 5 \bullet 3 \bullet 8 = 120;\]

\[11)\ C_{100}^{98} = \frac{100!}{98!(100 - 98)!} =\]

\[= \frac{100 \bullet 99 \bullet 98!}{2!} = \frac{100 \bullet 99}{2} =\]

\[= 50 \bullet 99 = 4950;\]

\[12)\ C_{70}^{2} = \frac{70!}{2!(70 - 2)!} =\]

\[= \frac{70 \bullet 69 \bullet 68!}{2 \bullet 68!} = 35 \bullet 69 = 2415.\]