Question

Determinati valorile naturale ale lui x astfel incat:
combinari de 10 luate cate n sa fie mai mic sau egal decant combinari de 10 luate cate n-2

Answer 1

(C10^n≤C10^(n-2)
10!/n!*(10-n)!≤10!/(n-2)!*(10-(n-2))! =>
1/n!*(10-n)!≤1/(n-2)!*(8-n)!=>
n!*(10-n)!≥(n-2)!*(8-n)
(n-2)!*(n-1)*n*(10-n)!≥(n-2)!*(8-n)!
(n-1)*n*(8-n)!*(9-n)*(10-n)≥(8-n)!
(n-1)*n≥(9-n)*(10-n)
n²-n≥90-19n+n²
18n≥90
n≥5