Question

Combinari de 9 luate cate 7, combinari de 8 luate cate 5 si aranjamente de 7 luate cate 3

Answer 1

$C_{9}^{7} = \frac{9!}{7!(9 - 7)!} = \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9}{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 2!} = \frac{8 \times 9}{1 \times 2} = \frac{72}{2} = 36$

$C_{8}^{5} = \frac{8!}{5!(8 - 5)!} = \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8}{1 \times 2 \times 3 \times 4 \times 5 \times 3!} = \frac{6 \times 7 \times 8}{1 \times 2 \times 3} = 7 \times 8 = 56$

$A_{7}^{3} = \frac{7!}{(7 - 3)!} = \frac{1 \times 2 \times 3 \times 4\times 5 \times 6 \times 7}{4!} = \frac{1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7}{1 \times 2 \times 3 \times 4} = 5 \times 6 \times 7 = 210$