Answer
0.0023
Step-by-step explanation:
[tex]\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{ = }\frac{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} \\ \frac{12C_9}{12P_5}\text{ = }\frac{220}{95040} \\ \frac{12C_9}{12P_5}_{}=\text{ 0.0023} \end{gathered}[/tex]
