Question

Calcule o valor de C12,5+C8,4-C7,3.

Answer 1

Lembrando que combinação simples é:

$C_{n, p}= \frac{n!}{(n-p)!p!}$

Assim:

$C_{12, 5} + C_{8, 4} - C_{7, 3} \\ \\ \frac{12!}{(12-5)!5!} + \frac{8!}{(8-4)!4!} - \frac{7!}{(7-3)!3!} \\ \\ \frac{12!}{7!5!} + \frac{8!}{4!4!} - \frac{7!}{4!3!} \\ \\ \frac{12.11.10.9.8.7!}{7!.5.4.3.2.1} + \frac{8.7.6.5.4!}{4!.4.3.2.1} - \frac{7.6.5.4!}{4!.3.2.1} \\ \\ \frac{12.11.10.9.8}{5.4.3.2.1} + \frac{8.7.6.5}{4.3.2.1} - \frac{7.6.5}{3.2.1} \\ \\ \frac{95040}{120} + \frac{1680}{24} - \frac{210}{6} \\ \\ 792 + 70 - 35 \\ \\ 827$