Question

Cate numere naturale se pot scrie cu cifrele 1, 2,3 ,4 si 1, 2, 3, 4, 5.

Answer 1

$\displaystyle Pentru~primul~caz,nr~de~numere~naturale~ce~se~pot~forma~este: \\ \\ N_1=A_{4}^1+A_{4}^2+A_{4}^3+A_{4}^4=\frac{4!}{(4-1)!}+\frac{4!}{(4-2)!}+\frac{4!}{(4-3)!}+\frac{4!}{(4-4)!}= \\ 4+3*4+4!+4!=64 \\ \\ Pentru~al~doilea~caz: \\ \\ N_2=A_5^1+A_5^2+A_5^3+A_5^4+A_5^5=\frac{5!}{(5-1)!}+\frac{5!}{(5-2)!}+\frac{5!}{(5-3)!}+\frac{5!}{(5-4)!}+ \\ +\frac{5!}{(5-5)!}=5+4*5+3*4*5+5!+5!=325$