A company has 500 employees, and 60% of them have children. Suppose that we randomly select 4 of these employees. What is the probability that exactly 3 of the 4 employees selected have children? We know that 300 of these employees have children. I tried to figure it out, how to work with the binomial equation by the given's

A company has 500 employees, and 60% of them have children.
Suppose that we randomly select 4 of these employees.
What is the probability that exactly 3 of the 4 employees selected have children?
We know that 300 of these employees have children.
I tried to figure it out, how to work with the binomial equation by the given's
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Julianna Crawford
Step 1
The probability that the first person picked has kids is $\frac{300}{500}$. Conditional on that, the probability that the second person picked has kids is $\frac{299}{499}$. Conditional on all that, the probability the third person has kids is $\frac{298}{498}$. Conditional on all that, the probability the fourth person doesn't have kids is $\frac{200}{497}$. So multiply these together and scale by 4 (since the person without kids could have been any of the four).
Step 2
An alternative perspective: the number of quadruples where exactly three have kids is $\left(\genfrac{}{}{0}{}{300}{3}\right)\cdot \left(\genfrac{}{}{0}{}{200}{1}\right)$. There are $\left(\genfrac{}{}{0}{}{500}{4}\right)$ quadruples in total, so divide the two to get the probability.