Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 551

\[1)\ P_{5}(2) =\]

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

\[= \frac{5!}{2!(5 - 2)!} \bullet \frac{1}{6^{2}} \bullet \frac{5^{3}}{6^{3}} =\]

\[= \frac{5 \bullet 4 \bullet 3!}{2 \bullet 3!} \bullet \frac{5^{3}}{6^{5}} = \frac{5^{4} \bullet 2}{6^{5}} =\]

\[= \frac{625 \bullet 2}{7776} = \frac{625}{3888}.\]

\[Ответ:\ \ \frac{625}{3888}.\]

\[2)\ P_{5}(4) =\]

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

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

\[= \frac{5 \bullet 4!}{4! \bullet 1} \bullet \frac{5}{6^{5}} = \frac{5^{2}}{6^{5}} = \frac{25}{7776}.\]

\[Ответ:\ \ \frac{25}{7776}.\]