Question

evaluate the expression . express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

0.0023

Explanation:

`\begin{gathered} \text{Given the following expression} \\ \frac{12_{}C_9}{12P_5} \\ \text{According to the standard formula of combination and permutation} \\ ^nC_r\text{ = }\frac{n\text{!}}{(n\text{ - r)!r!}} \\ ^(12)C_9\text{ = }\frac{12!}{(12\text{ - 9)! 9!}} \\ 12C_9\text{ = }(12!)/(3!9!) \\ 12C_9\text{ = }\frac{12\text{ x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x1}}{3\text{ x 2 x 1! 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1}} \\ 12C_9\text{ = }\frac{12\text{ x 11 x 10}}{6} \\ 12C_9\text{ = 220} \\ \\ 12P_5\text{ = }\frac{12!}{(12\text{ - 5)!}} \\ 12P_5\text{ = }\frac{12\text{ x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x1}}{7\text{ x 6 x 5 x 4 x 3 x 2 x 1}} \\ 12P_5\text{ = 12 x 11 x 10 x 9 x 8} \\ 12P_5\text{ = 95,040} \\ (12C_9)/(12P_5)\text{ = }(220)/(95040) \\ (12C_9)/(12P_5)_{}=\text{ 0.0023} \end{gathered}`