Задание 1 Найдите значение выражения: 3P12 - P11 - 1) 7 P10 2) 2 A 5 3

Задание 1

1) \(\frac{3P_{12} - P_{11}}{7P_{10}}\) = \(\frac{3 \cdot 12! - 11!}{7 \cdot 10!}\) = \(\frac{11! \cdot (3 \cdot 12 - 1)}{7 \cdot 10!}\) = \(\frac{11! \cdot 35}{7 \cdot 10!}\) = \(\frac{11 \cdot 10! \cdot 5}{10!}\) = 11 \cdot 5 = 55

2) \(\frac{A_5^2}{C_6^3}\) = \(\frac{\frac{5!}{(5-2)!}}{\frac{6!}{3!(6-3)!}}\) = \(\frac{\frac{5!}{3!}}{\frac{6!}{3!3!}}\) = \(\frac{5 \cdot 4}{ \frac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1}}\) = \(\frac{20}{20}\) = 1