جد قيمة ما يلي: ${\mathrm{P}}_3^7$

${\mathrm{P}}_3^7=\frac{7!}{(7-3)!}=\frac{\left(7\right)\left(6\right)\left(5\right)4!}{4!}=210$

تدرب وحل التمرينات

جد قيمة كل مما يأتي:

(10)- $2!\times 6!$

$2!\times 6!=(2\times 1)\times (6\times 5\times 4\times 3\times 2\times 1)=2\times 720=1440$

(11)- $4!\times 3!$

$4!\times 3!=\left[\right(4\left)\right(3\left)\right(2\left)\right(1\left)\right]\left[\right(3\left)\right(2\left)\right(1\left)\right]=144$

(12)- $0!\times 1!$

$0!\times 1!=\left(1\right)\times \left(1\right)=1$

(13)- ${\mathrm{P}}_0^{10}$

${\mathrm{P}}_0^{10}=1$

(14)- $\left(\begin{array}{c}10\\ 1\end{array}\right)$

$\left(\begin{array}{l}10\\ 1\end{array}\right)=10$

(15)- ${\mathrm{C}}_5^9$

${\mathrm{C}}_5^9=\frac{9\times 8\times 7\times 6\times 5}{5\times 4\times 3\times 2\times 1}=9\times 7\times 2=126$

(16)- ${\mathrm{P}}_3^7$

${\mathrm{P}}_3^7=\frac{7!}{(7-3)!}=\frac{\left(7\right)\left(6\right)\left(5\right)4!}{4!}=210$

(17)- ${\mathrm{P}}_1^{15}$

${\mathrm{P}}_1^{15}=15$

(18)- ${\mathrm{C}}_{100}^{100}$

${\mathrm{C}}_{100}^{100}=1$