примеры с факториалами, 40 баллов...

uehehqjsisusu @uehehqjsisusu

August 2022 1 4 Report

примеры с факториалами, 40 баллов

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sangers1959

Verified answer

Объяснение:

A)

$\frac{P_{20}}{A_{20}^{15}}-\frac{A_{20}^5}{C_{20}^5}=\frac{20!}{\frac{20!}{(20-15)!} }-\frac{\frac{20!}{(20-5)!} }{\frac{20!}{(20-5)!*5!} }=5!-5!=0.$

B)

$C_7^5*P_3=\frac{7!}{(7-5)!*5!}*3!=\frac{5!*6*7}{5!*2!}*1*2*3=3*7*6=126.$

C)

$A_x^5=336*C_{x-2}^{x-5}\ \ \ \ x>0\ \ \ \ x-2>0\ \ \ \ x-5>0\ \ \ \ \Rightarrow\ \ \ \ x>5.\\\frac{x!}{(x-5)!} =336*\frac{(x-2)!}{(x-2-(x-5))!*(x-5)!} \\\frac{(x-2)!*(x-1)*x}{(x-5)!}=336*\frac{(x-2)!}{3!*(x-5)!} \\(x-1)*x=\frac{336}{6}\\x^2-x=56 \\x^2-x-56=0\\D=225\ \ \ \ \sqrt{D}=15\\x_1=-7\notin\ \ \ \ x_2=8\in .$

Ответ: x=8.

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