Question

un antrenor are la dispozitie 10 jucatori.In cate moduri poate forma o echipa formata din 6 jucatori?​

Answer 1

Răspuns:

210 moduri

Explicație pas cu pas:

Se aplica formula combinarilor.

Avem combinari de 10 luate cate 6.

$\displaystyle\\C_{10}^{6} = \frac{10!}{6! \times (10-6)!}$

$\displaystyle\\C_{10}^{6} = \frac{10!}{6! \times 4!} = \frac{10 \times 9 \times 8 \times 7 \times 6!}{6! \times 4!}$

$\displaystyle\\C_{10}^{6} = \frac{10 \times 9 \times 8 \times 7}{4!} = \frac{90 \times 8 \times 7}{1 \times 2 \times 3 \times 4}$

$\displaystyle\\C_{10}^{6}=\frac{630 \times 8}{24}^{(8}$

$\displaystyle\\C_{10}^{6} = \frac{630}{3} = 210$