Question

Помогите пожалуйста ​

Answer 1

Ответ:

Объяснение:

$P_n=n!\\C_n^k=\frac{n!}{k!(n-k)!}\\A_n^k=\frac{n!}{(n-k)!}$

5

$C_{17}^8+C_{17}^9=\frac{17!}{8!(17-8)!} +\frac{17!}{9!(17-9)!} =\frac{17!}{8!9!} +\frac{17!}{9!8!} =\frac{2*17!}{8!9!} =\frac{2*10*11*12*13*14*15*16*17}{8!} =11*13*2*5*2*17=48620$

$C_{71}^5-C_{70}^4=\frac{71!}{5!(71-5)!} -\frac{70!}{4!(70-4)!} =\frac{71!}{5!66!} -\frac{70!}{4!66!} =\frac{71*70!-5*70!}{5!66!} =\frac{70!*66}{5!66!} =14*69*68*67*66=290472336$

6

$A_x^2=\frac{x!}{(x-2)!}=\frac{x*(x-1)*(x-2)!}{(x-2)!} =x*(x-1) \\38x=x*(x-1)\\x^2-x-38x=0\\x(x-39)=0\\x_1=0;x_2=39$