Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 550

\[1)\ P_{10}(4) = C_{10}^{4} \bullet {0,5}^{4} \bullet {0,5}^{10 - 4} =\]

\[= \frac{10!}{4!(10 - 4)!} \bullet {0,5}^{10} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7 \bullet 6!}{4 \bullet 3 \bullet 2 \bullet 6!} \bullet \frac{1}{2^{10}} =\]

\[= \frac{5 \bullet 3 \bullet 2 \bullet 7}{2^{10}} = \frac{105}{512}.\]

\[Ответ:\ \ \frac{105}{512}.\]

\[2)\ P_{10}(5) = C_{10}^{5} \bullet {0,5}^{5} \bullet {0,5}^{10 - 5} =\]

\[= \frac{10!}{5!(10 - 5)!} \bullet {0,5}^{10} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7 \bullet 6 \bullet 5!}{5 \bullet 4 \bullet 3 \bullet 2 \bullet 5!} \bullet \frac{1}{2^{10}} =\]

\[= \frac{3 \bullet 2 \bullet 7 \bullet 6}{2^{10}} = \frac{63}{256}.\]

\[Ответ:\ \ \frac{63}{256}.\]