Question

In cate moduri poate fi format un comitet de 3 elevi, daca in clasa sunt 15 elevi?

Answer 1

Combinari de n luate cate k=n!/k!(n-k)!

C₁₅³ - combinari de 15 luate cate 3

C₁₅³=15!/(3!x(15 - 3)!) = 15!/(3!x12!) = simplificam prin 12!

C₁₅³= (13×14×15)/(1×2×3) = 455 moduri

Answer 2

nu conteaza ordinea (functia fiecaruia, 'aranjarea " ) este un comitet.. toti egali

deci combinari, nu aranjamente

Cde 15 luatecate3=15!/(12!*3!)=12!*13*14*15/12!*3!=13*14*15/3!=13*14*15/2*3=13*7*5=

=91*5=455 moduri