[tex]\text{Proprietati folosite:}\\\\C_{n}^k = C_{n}^{n-k}\\\\C_{n}^k = C_{n-1}^k+C_{n-1}^{k-1}\\\\\\\text{Rezolvare:}\\\\C_4^0 - C_4^1+C_4^2-C_4^3+C_4^4 =\\\\ =C_4^0+C_{4}^4-C_{4}^1-C_{4}^3+C_{4}^2 \\ \\ =2\cdot C_{4}^0 - 2\cdot C_{4}^1+C_{4}^2\\ \\ = 2\cdot 1-2\cdot 4+C_{3}^2+C_{3}^1\\ \\ = 2-8+3+3\\\\ = 0[/tex]
