Question

помогите вычислить!! во вложениях)
заранее спасибо)

Answer 1

$b);frac{P_6}{A_{10}^7}cdotleft(C_7^5+C_7^3right)=frac{6!}{frac{10!}{3!}}cdotleft(frac{7!}{5!2!}+frac{7!}{3!4!}}right)=frac{6!3!}{10!}cdotleft(frac{6cdot7}{1cdot2}+frac{5cdot6cdot7}{1cdot2cdot3}right)=\=frac{1cdot2cdot3}{7cdot8cdot9}cdotleft(21+35right)=frac1{84}cdot56=frac23$
$c);frac{P_{k+1}}{P_{k-n}cdot A_{k-1}^{n-1}}=frac{(k+1)!}{(k-n)!frac{(k-1)!}{(n-1)!(k-1-n+1)!}}=frac{(k+1)!}{(k-n)!frac{(k-1)!}{(n-1)!(k-n)!}}=\=frac{(k+1)!(n-1)!}{(k-1)!}=kcdot(k+1)cdot(n-1)!$
$d);frac{A_{n+k}^{n+2}+A_{n+k}^{n+1}}{A_{n+k}^n}=frac{frac{(n+k)!}{(n+k-n-2)!}+frac{(n+k)!}{(n+k-n-1)!}}{frac{(n+k)!}{(n+k-n)!}}=frac{frac{(n+k)!}{(k-2)!}+frac{(n+k)!}{(k-1)!}}{frac{(n+k)!}{k!}}=\=frac{frac{(k-1)cdot(n+k)!+(n+k)!}{(k-1)!}}{frac{(n+k!)}{k!}}=frac{k!cdot(n+k)!cdot((k-1)+1)}{(k-1)!(n+k)!}=frac{k!cdot k}{(k-1)!}=kcdot k=k^2$