Question

22 elevi dintre care 12 fete si 10 baieti .in cate moduri se poate forma un comitet din 3 fete si 2 baieti?


..Combinari de 12 luate cate 3 × C de 10 luate cate 2??)

Answer 1

   
$n_{moduri} =C_{12}^3 \cdot C_{10}^2 = \\ \\ = \frac{12 \,\cdot \,11\,\cdot \,10}{1\,\cdot \, 2 \,\cdot \,3}\,\cdot \, \frac{10\,\cdot \,9}{1\,\cdot \, 2 }= \\ \\ =(2 \,\cdot \,11\,\cdot \,10)\,\cdot \,(5\,\cdot \,9)=220\,\cdot \,45= \boxed{9900~moduri}$