Question

Комбинаторика. Вычислить 1. 9!5!/10! 2. Р8-Р7/Р6 3. А6^3 4. С12^6 ПЖ

Answer 1

$\displaystyle \tt 1). \ \ \frac{9!\cdot5!}{10!}=\frac{9!\cdot2\cdot3\cdot4\cdot5}{9!\cdot10}=12\\\\\\2). \ \ \frac{P_{8}-P_{7}}{P_{6}}=\frac{8!-7!}{6!}=\frac{6!\cdot(7\cdot8-7)}{6!}=56-7=49\\\\\\3). \ \ A_{6}^{3}=\frac{6!}{(6-3)!}=\frac{3!\cdot4\cdot5\cdot6}{3!}=120\\\\\\4). \ \ C_{12}^{6}=\frac{12!}{6!\cdot(12-6)!}=\frac{6!\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{6!\cdot2\cdot3\cdot4\cdot5\cdot6}=7\cdot11\cdot12=924$