Question

Combinação simples Calcule: a) C 8,5 b) C 10,3 c) C n, n – 2

Answer 1

$\tt{a)}~\sf{C_{8,5}=\dfrac{8\cdot7\cdot \diagup\!\!\!\!6\cdot \diagup\!\!\!\!5\cdot \diagup\!\!\!\!4}{ \diagup\!\!\!\!5\cdot \diagup\!\!\!\!4\cdot \diagup\!\!\!\!3\cdot \diagup\!\!\!\!2\cdot1}=56}\\\tt{b)}~\sf{C_{10,3}=\dfrac{10\cdot \diagup\!\!\!\!9^3\cdot \diagup\!\!\!\!8^4}{ \diagup\!\!\!\!3\cdot \diagup\!\!\!\!2\cdot1}=120}\\\tt{c)}~\sf{C_{n, n-2}=\dfrac{n!}{(n-2)!\cdot(n-[n-2])!}}\\\sf{\dfrac{n(n-1) \diagup\!\!\!\!{(n-2)!}}{\diagup\!\!\!\!(n-2)!\cdot2!}}\\\sf{C_{n,n-2}=\dfrac{n(n-1)}{2}}$