Question

Cate numere de trei cifre distincte se pot forma utilizand cifrele 2,3,4,si 5 ?

Answer 1

 

$\displaystyle\bf\\Avem~cifrele:~~2,~3,~4,~si~5~~~in~total~4~cifre. \\\\Cate~numere~de~3~cifre~dinstincte~formam~cu~cele~4~cifre?\\\\Rezolvare:\\\\Metoda~1\\Folosim~formula:\\A_n^k=\underbrace{\bf n\cdot(n-1)\cdot(n-2)\cdots(n-k+1)}_{k~factori}\\\\\\A_4^3=4\times3\times2=\boxed{\bf24~de~numere~de~3~cifre}\\\\\\Metoda~2\\Folosim~formula:\\\\A_n^k=\frac{n!}{(n-k)!}\\\\\\A_4^3=\frac{4!}{(4-3)!}=\frac{4!}{1!}=\frac{1\times2\times3\times4}{1}=\frac{24}{1} =\boxed{\bf24~de~numere~de~3~cifre}$