Question

Doresc putin ajutor la aceste exerciti
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Answer 1

Răspuns:

Explicație pas cu pas:

$C_{n} ^{k} =\frac{n!}{k!(n-k)!}\\ \\A_{n} ^{k} =\frac{n!}{(n-k)!}\\\\C_{n} ^{k} =C_{n} ^{n-k}$

d)

$C_{x+8} ^{x+3} =C_{x+8} ^{5} =\frac{(x+8)!}{5!(x\\+3)!} \\\\A_{x+6} ^{3} =\frac{(x+6)!}{(x+3)!} \\\\\frac{(x+8)!}{5!(x+3)!}=5\frac{(x+6)!}{(x+3)!}\\ \\ \frac{(x+6)!(x+7)(x+8)}{5!(x+3)!}=5\frac{(x+6)!}{(x+3)!}\\ \\ (x+7)(x+8) = 600....$

e)

$\\ \frac{x!}{(x-6)!}-24x\frac{x!}{4!(x-4)!} =11\frac{x!}{(x-4)!} \\ \\\\ \frac{1}{(x-5)(x-6)}-\frac{24x}{4!} =11 \\ \\ \\\frac{1}{(x-5)(x-6)}=11 +x\\ \\ \\(x+11)(x-5)(x-6)=1$