Combinations and Probability
An employee group requires 6 people be chosen for a committee from a group of 17 employees. Determine the following probabilities of randomly drawn committee of 6 employees.

Write your answers as percents rounded to 4 decimal places.
The employee group has 6 women and 11 men.
What is the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men?
$\%$
The committee requires that exactly 3 people from Customer Service serve on the committee. There are 4 people in Customer Service.

What is the probability that exactly 3 of the people chosen for the committee are from Customer Service?

Step 1 ：The total number of ways to choose 6 people out of 17 is given by the combination formula \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial. So, the total number of ways to choose 6 people out of 17 is \(C(17, 6)\).

Step 2 ：Calculate \(C(17, 6) = \frac{17!}{6!(17-6)!} = 12376\).

Step 3 ：The number of ways to choose 3 women out of 6 is \(C(6, 3)\), and the number of ways to choose 3 men out of 11 is \(C(11, 3)\).

Step 4 ：Calculate \(C(6, 3) = \frac{6!}{3!(6-3)!} = 20\) and \(C(11, 3) = \frac{11!}{3!(11-3)!} = 165\).

Step 5 ：So, the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men is \(\frac{C(6, 3) * C(11, 3)}{C(17, 6)}\).

Step 6 ：Calculate the probability as \(\frac{(20 * 165)}{12376} = 0.2668\) or 26.68%.

Step 7 ：\(\boxed{0.2668}\) or \(\boxed{26.68\%}\) is the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men.

Step 8 ：The number of ways to choose 3 people from Customer Service out of 4 is \(C(4, 3)\), and the number of ways to choose the remaining 3 people out of the 13 not in Customer Service is \(C(13, 3)\).

Step 9 ：Calculate \(C(4, 3) = \frac{4!}{3!(4-3)!} = 4\) and \(C(13, 3) = \frac{13!}{3!(13-3)!} = 286\).

Step 10 ：So, the probability that exactly 3 of the people chosen for the committee are from Customer Service is \(\frac{C(4, 3) * C(13, 3)}{C(17, 6)}\).

Step 11 ：Calculate the probability as \(\frac{(4 * 286)}{12376} = 0.0924\) or 9.24%.

Step 12 ：\(\boxed{0.0924}\) or \(\boxed{9.24\%}\) is the probability that exactly 3 of the people chosen for the committee are from Customer Service.