Question

calcule C5,3/C3,2+C7,3

Answer 1

C5,3 / C3,2+C7,3

5.4.3/3! / 3.2/2!+7.6.5/3!

5.4 3/6 / 3.2/2+7.6.5/6

10 / 3+35 = 10/38 = 5/19 ✓

Answer 2

Como está escrito no enunciado não da pra identificar se o o denominador é apenas C3,2 ou se é C3,2+C7,3.

Assim irei colocar as duas formas, considere a que esteja de acordo:

1ª forma:

$\frac{C_{5,3}}{C_{3,2}+C_{7,3}}\\\\\\\frac{\frac{5!}{3!.(5-3)!}}{\frac{3!}{2!.(3-2)!}+\frac{7!}{3!.(7-3)!}}\\\\\\\frac{\frac{120}{6\,.\,2}}{\frac{6}{2\,.\,1}+\frac{5040}{6\,.\,24}}\\\\\\\frac{\frac{120}{12}}{\frac{6}{2}+\frac{5040}{144}}\\\\\\\frac{10}{3+35}\\\\\\\frac{5}{19}$

2ªforma:

$\frac{C_{5,3}}{C_{3,2}}+C_{7,3}\\\\\\\frac{\frac{5!}{3!.(5-3)!}}{\frac{3!}{2!.(3-2)!}}+\frac{7!}{3!.(7-3)!}\\\\\\\frac{\frac{120}{6\,.\,2}}{\frac{6}{2\,.\,1}}+\frac{5040}{6\,.\,24}\\\\\\\frac{\frac{120}{12}}{\frac{6}{2}}+\frac{5040}{144}\\\\\\\frac{10}{3}+35\\\\\\\frac{10+3\,.\,35}{3}\\\\\\\frac{115}{3}$