204. Вычислите: a) 5!; б) 10!/8!; в) A³₅; г) A⁵₁₀; д) A⁹₁₀.

а) 5! = 5 × 4 × 3 × 2 × 1 = 120 б) $$\frac{10!}{8!} = \frac{10 \times 9 \times 8!}{8!} = 10 \times 9 = 90$$ в) $$A_5^3 = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 5 \times 4 \times 3 = 60$$ г) $$A_{10}^5 = \frac{10!}{(10-5)!} = \frac{10!}{5!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5!}{5!} = 10 \times 9 \times 8 \times 7 \times 6 = 30240$$ д) $$A_{10}^9 = \frac{10!}{(10-9)!} = \frac{10!}{1!} = 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3628800$$ Ответ: a) 120 б) 90 в) 60 г) 30240 д) 3628800