5. Найти а) $$C_{15}^3$$; б) $$A_7^5$$; в) $$A_{20}^5 \div C_{20}^5$$.

1. а) $$C_{15}^3 = \frac{15!}{3!(15-3)!} = \frac{15!}{3!12!} = \frac{15 \times 14 \times 13}{3 \times 2 \times 1} = 455$$

2. б) $$A_7^5 = \frac{7!}{(7-5)!} = \frac{7!}{2!} = 7 \times 6 \times 5 \times 4 \times 3 = 2520$$

3. в) $$A_{20}^5 = \frac{20!}{(20-5)!} = \frac{20!}{15!} = 20 \times 19 \times 18 \times 17 \times 16 = 1860480$$ $$C_{20}^5 = \frac{20!}{5!(20-5)!} = \frac{20!}{5!15!} = \frac{20 \times 19 \times 18 \times 17 \times 16}{5 \times 4 \times 3 \times 2 \times 1} = 15504$$ $$\frac{A_{20}^5}{C_{20}^5} = \frac{1860480}{15504} = 120$$

Ответ: а) 455; б) 2520; в) 120