Сравни числа: a) C²₅ и C³₅

Сравним числа: a) $C_5^2$ и $C_5^3$ $C_5^2 = \frac{5!}{2!(5-2)!} = \frac{5!}{2!3!} = \frac{5 \cdot 4}{2 \cdot 1} = 10$ $C_5^3 = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5 \cdot 4}{2 \cdot 1} = 10$ Значит, $C_5^2 = C_5^3$ б) $C_7^2$ и $C_7^5$ $C_7^2 = \frac{7!}{2!(7-2)!} = \frac{7!}{2!5!} = \frac{7 \cdot 6}{2 \cdot 1} = 21$ $C_7^5 = \frac{7!}{5!(7-5)!} = \frac{7!}{5!2!} = \frac{7 \cdot 6}{2 \cdot 1} = 21$ Значит, $C_7^2 = C_7^5$ в) $C_{21}^1$ и $C_{21}^{20}$ $C_{21}^1 = \frac{21!}{1!(21-1)!} = \frac{21!}{1!20!} = 21$ $C_{21}^{20} = \frac{21!}{20!(21-20)!} = \frac{21!}{20!1!} = 21$ Значит, $C_{21}^1 = C_{21}^{20}$ г) $C_{12}^5$ и $C_{12}^7$ $C_{12}^5 = \frac{12!}{5!(12-5)!} = \frac{12!}{5!7!} = \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 792$ $C_{12}^7 = \frac{12!}{7!(12-7)!} = \frac{12!}{7!5!} = \frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 792$ Значит, $C_{12}^5 = C_{12}^7$ **Ответ:** а) $C_5^2 = C_5^3$ б) $C_7^2 = C_7^5$ в) $C_{21}^1 = C_{21}^{20}$ г) $C_{12}^5 = C_{12}^7$