Question

Calcule C7,3 x C8,2​

Answer 1

$C_{7,3}~\times~C_{8,2}~=~\dfrac{7!}{3!~.~(7-3)!}~\times~\dfrac{8!}{2!~.~(8-2)!}\\\\\\C_{7,3}~\times~C_{8,2}~=~\dfrac{7~.~6~.~5~.~4!}{3~.~2~.~1~.~4!}~\times~\dfrac{8~.~7~.~6!}{2~.~1~.~6!}\\\\\\C_{7,3}~\times~C_{8,2}~=~\dfrac{7~.~6\!\!\!\backslash~.~5~.~4!\!\!\!\backslash}{3\!\!\!\backslash~.~2\!\!\!\backslash~.~1~.~4!\!\!\!\backslash}~\times~\dfrac{^{^4}8\!\!\!\backslash~.~7~.~6!\!\!\!\backslash}{~\,2\!\!\!\backslash~.~1~.~6!\!\!\!\backslash}$

$C_{7,3}~\times~C_{8,2}~=~(7~.~5)~\times~(4~.~7)\\\\\\C_{7,3}~\times~C_{8,2}~=~(35)~\times~(28)\\\\\\\boxed{C_{7,3}~\times~C_{8,2}~=~980}$

Answer 2

Explicação passo-a-passo:

Combinações :

$\boxed{\boxed{\mathsf{C_{n,p}~=~\dfrac{n!}{p!(n-p)! }}}}$

$\mathsf{C_{7,3} \times C_{8,2}~=~?? }$

Aplicando a FÓRMULA de COMBINACÃO :

$\mathsf{C_{7,3} \times C_{8,2}~=~\dfrac{7!}{3!(7-3)!}\times\dfrac{8!}{2!(8-2)!} }$

$\mathsf{C_{7,3} \times C_{8,2}~=~\dfrac{7.6.5.\cancel{4!}}{3!.\cancel{4!}} \times \dfrac{8.7.\cancel{6!}}{2!.\cancel{6!}} }$

$\mathsf{ C_{7,3} \times C_{8,2}~=~\dfrac{7.\cancel{6}.5} {\cancel{3}.2.1} \times \dfrac{\cancel{8}.7}{\mathsf{\cancel{2}.1}} }$

$\mathsf{ C_{7,3} \times C_{8,2}~=~\dfrac{7.\cancel{2}.5} {\cancel{2}.1} \times \dfrac{4.7} {1} }$

$\mathsf{C_{7,3} \times C_{8,2}~=~ \dfrac{7.5}{1} \times (4.7) }$

$\mathsf{ C_{7,3} \times C_{8,2}~=~(7.5).(4.7) }$

$\mathsf{ C_{7,3} \times C_{8,2}~=~980 }$