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A town recently dismissed eight employees in order to meet their new budget reductions. The town had six employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50? Express your answer as a fraction or decimal number rounded to four decimal places

A town recently dismissed eight employees in order to meet their new budget reductions The town had six employees over 50 years of age and 18 under 50 If the di class=

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Solution:

Given:

[tex]\begin{gathered} Total\text{ dismissed}=8 \\ \\ \\ Over\text{ 50}=6 \\ Under\text{ 50}=18 \\ Total\text{ employees}=24 \end{gathered}[/tex]

If the dismissed employees were selected at random what is the probability that exactly 6 employees were over 50 will be;

[tex]\begin{gathered} \frac{^6C_6\times^{18}C_2}{^{24}C_8}=\frac{1\times153}{735471} \\ =\frac{153}{735471} \\ =\frac{1}{4807} \end{gathered}[/tex]

Therefore, the probability that exactly 6 employees were over 50 will be;

[tex]\frac{1}{4807}[/tex]

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