Question

in how many ways can you select 5 toy cars to race out of a box containing 14 toy cars?

\\_nc_r = \frac{n!}{r!(n-r)!}\\

Explanation:

Identify parameters

$$ n = 14,\quad r = 5 $$

Apply combination formula

$$ {}_{14}C_{5} = \frac{14!}{5!(14-5)!} = \frac{14!}{5! \cdot 9!} $$

Calculate final value

$$ {}_{14}C_{5} = \frac{14 \times 13 \times 12 \times 11 \times 10}{5 \times 4 \times 3 \times 2 \times 1} = 2002 $$

Answer:

2002