أوجد ناتج ما يلي:  ${\mathrm{C}}_3^8$

${\mathrm{C}}_3^8=\frac{8!}{5!3!}=\frac{\left(8\right)\left(7\right)\left(6\right)5!}{5!\times 3\times 2\times 1}=56$

تأكد من فهمك

جد قيمة كل مما يأتي:

(1)- $4!\times 2!$

$4!\times 2!=(4\times 3\times 2\times 1)\times (2\times 1)=24\times 2=48$

(2)- $\left(3+2\right)!$

$(3+2)!=5!=5\times 4\times 3\times 2\times 1=120$

(3)- $\frac{9!}{6!}$

$\frac{9!}{6!}=\frac{9\times 8\times 7\times 6!}{6!}=9\times 8\times 7=504$

(4)- $\left(7-5\right)!$

$(7-5)!=2!=2\times 1=2$

(5)- $3!+2!$

$3!+2!=(3\times 2\times 1)+(2\times 1)=6+2=8$

(6)- ${\mathrm{P}}_8^8$

${\mathrm{P}}_8^8=8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320$

(7)- ${\mathrm{P}}_4^{10}$

${\mathrm{P}}_4^{10}=10\times 9\times 8\times 7=5040$

(8)- ${\mathrm{C}}_3^8$

${\mathrm{C}}_3^8=\frac{8!}{5!3!}=\frac{\left(8\right)\left(7\right)\left(6\right)5!}{5!\times 3\times 2\times 1}=56$

(9)- $\left(\begin{array}{c}9\\ 0\end{array}\right)$

$\left(\begin{array}{l}9\\ 0\end{array}\right)=1$