Question

Комбинаторика, решите пожалуйста.

Answer 1

$\frac{6!}{8!} = \frac{6!}{6! \times 7 \times 8} = \frac{1}{7 \times 8} = \frac{1}{56}$

$\frac{14!}{12!} = \frac{12! \times 13 \times 14}{12!} = 182$

$\frac{25!}{23! \times 5!} = \frac{23! \times 24 \times 25}{23! \times 2 \times 3 \times 4 \times 5} = \frac{6 \times 5}{6} = 5$

$\frac{P_{7} - P_{6}}{P_{5}} = \frac{7! - 6!}{5!} = \frac{6!(7 - 1)}{5!} = \frac{5! \times6 \times 6}{5!} = 36$

$A_{6}^{4} = \frac{6!}{(6 - 4)!} = \frac{6!}{2!} = \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6}{1 \times 2} = \\ = 3 \times 4 \times 5 \times 6 = 360$

$C_{7}^{3} = \frac{7!}{(7 - 3)! \times 3!} = \frac{7!}{4! \times 3!} = \frac{4! \times 5 \times 6 \times 7}{4! \times 2 \times 3} = 5 \times 7 = 35$