Упр.1.64 ГДЗ Никольский 10 класс (Алгебра)

Используем формулу сочетаний:

$$C_n^k=\frac{n!}{k!(n-k)!}.$$

1. $$C_{10}^9=C_{10}^{10-9}=C_{10}^1=\frac{10!}{1!\,9!}=10.$$

2. $$C_{10}^8=C_{10}^{10-8}=C_{10}^2=\frac{10!}{2!\,8!}=\frac{10\cdot 9}{2}=45.$$

3. $$C_{12}^{10}=C_{12}^{12-10}=C_{12}^2=\frac{12!}{2!\,10!}=\frac{12\cdot 11}{2}=66.$$

4. $$C_{12}^{11}=C_{12}^{12-11}=C_{12}^1=\frac{12!}{1!\,11!}=12.$$

5. $$C_{200}^{199}=C_{200}^{200-199}=C_{200}^1=\frac{200!}{1!\,199!}=200.$$

6. $$C_{2000}^{1999}=C_{2000}^{2000-1999}=C_{2000}^1=\frac{2000!}{1!\,1999!}=2000.$$

Ответ

$$10;\ 45;\ 66;\ 12;\ 200;\ 2000.$$