Question

calcule o valor de C6,4 - A5,3

Answer 1

$C_{6,4}-A_{5,3}= \dfrac{6!}{4!(6-4)!}- \dfrac{5!}{(5-3)!}\\\\\\ C_{6,4}-A_{5,3}= \dfrac{6!}{4!2!}- \dfrac{5!}{2!}\\\\\\ C_{6,4}-A_{5,3}= \dfrac{6\cdot5\cdot4\cdot3\cdot\not2}{4\cdot3\cdot2\cdot1!\not2!}- \dfrac{5\cdot4\cdot3\cdot\not2}{\not2}\\\\\\ C_{6,4}-A_{5,3}= \dfrac{360}{24}- 60\\\\\\ \Large\boxed{C_{6,4}-A_{5,3}=-45}}$