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.