Anniversary 63804

Out of 3,000 employees of a certain company, 1,800 are men. The management decided that on the occasion of the company's anniversary celebration, it will give special rewards to 10 randomly drawn employees. What is the probability that the sample will be equally distributed among 5 men and 5 women?

Correct answer:

p =  0.201

Step-by-step explanation:

$$\begin{gathered} n=3000 \\ m=1800 \\ z=n-m=3000-1800=1200 \\ {p}_1=\frac{m}{n}=\frac{1800}{3000}=\frac{3}{5}=0.6 \\ {p}_2=\frac{z}{n}=\frac{1200}{3000}=\frac{2}{5}=0.4 \\ {C}_5(10)=\left(\genfrac{}{}{0ex}{}{10}{5}\right)=\frac{10!}{5!(10-5)!}=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}=252 \\ p=\left(\genfrac{}{}{0ex}{}{10}{5}\right)\cdot p_1^5\cdot p_2^5=252\cdot {\frac{3}{5}}^5\cdot {\frac{2}{5}}^5=0.201 \end{gathered}$$

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