Question

*Sa se calculeze : a) C₂₂²⁰;C₁₀₀⁹⁸;C²ₓ

Answer 1

   
[tex]\displaystyle\\ \Big{C}_{22}^{20} = \Big{C}_{22}^{2} = \frac{\Big A_{22}^{2}}{\Big P_2} = \frac{22\times 21}{1\times 2}=11\times 21 = \boxed{231}\\\\\\ \Big{C}_{100}^{98} = \Big{C}_{100}^{2} = \frac{\Big A_{100}^{2}}{\Big P_2} = \frac{100\times 99}{1\times 2}=50\times 99 = \boxed{4950}\\\\\\ \Big{C}_{x}^{2} = \frac{\Big A_{x}^{2}}{\Big P_2} = \frac{x(x-1)}{1\times 2} = \boxed{\frac{x^2-x}{2}}[/tex]