Question

Помогите, пожалуйста ​

Answer 1

Пошаговое объяснение:

Все нужные формулы

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

1

$\frac{6!-4!}{3!} =\frac{6*5*4!-4!}{6}= \frac{(6*5-1)*4*3!}{3!} =(6*5-1)*4=29*4=116$

2

$\frac{(n-1)!}{(n-2)!} =\frac{(n-1)(n-2)!}{(n-2)!} =n-1$

3

$\frac{P_6-p_5}{p_4} =\frac{6!-5!}{4!} =\frac{6*5*4!-5*4!}{4!}=6*5-5=30-5=25$

$\frac{P_5+A_{11}^5}{C_4^3} =(P_5+A_{11}^5)/C_4^3=(5!+\frac{11!}{(11-5)!} )/\frac{4!}{3!(4-3)!} =(5!+\frac{11!}{6!} )/\frac{4!}{3!} =(5!+7*8*9*10*11)/4=2*3*5+7*2*9*10*11=30+13860=13890$

4

$A_8^4=\frac{8!}{(8-4)!} =\frac{8!}{4!} =5*6*7*8=1680$

$C_{10}^4=\frac{10!}{4!(10-4)!} =\frac{10! }{4!*6!} =\frac{7*8*9*10}{4!} =7*3*10=210$

$\frac{C_{12}^3}{A_{12}^3} =\frac{1}{3!} =\frac{1}{6}$

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

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