Question 6, 11.9.15 HW Score: $50 \%, 7$ of 14 points (x) Points: 0 of 1 Save The sales department at a certain company consists of four people, the manufacturing department consists of six people, and the accounting department consists of two people. Three people will be selected at random from these people and will be given gift certificates to a local restaurant. Determine the probability that two of those selected will be from the manufacturing department and one will be from the sales department. Assume that the selection is done without replacement. The probability that two of those selected will be from the manufacturing department and one will be from the sales department is $\square$. (Simplify your answer.)

Step 1 ：The problem is asking for the probability of a specific event in a random selection. The event is that two people are selected from the manufacturing department and one person is selected from the sales department.

Step 2 ：The total number of people is 12 (4 from sales, 6 from manufacturing, and 2 from accounting).

Step 3 ：The total number of ways to select 3 people from 12 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.

Step 4 ：The number of ways to select 2 people from the manufacturing department is \(C(6, 2)\), and the number of ways to select 1 person from the sales department is \(C(4, 1)\).

Step 5 ：The probability of the event is the number of favorable outcomes (the number of ways to select 2 people from manufacturing and 1 from sales) divided by the total number of outcomes (the number of ways to select 3 people from 12).

Step 6 ：Final Answer: The probability that two of those selected will be from the manufacturing department and one will be from the sales department is \(\boxed{0.2727}\).