Four engineers, A, B, C, and D, have been scheduled for job interviews at 10 A.M. on Friday, January 13, at Random Sampling, Inc. The personnel manager has scheduled the four for interview rooms 1, 2, 3, and 4, respectively. However, the managerâ€™s secretary does not know this, so assigns them to the four rooms in a completely random fashion (what else!). What is the probability that a. All four end up in the correct rooms? b. None of the four ends up in the correct room?

Solution : Step 1: It is given that 4 engineers A ,B ,C, D scheduled for job interviews. The personnel manager has scheduled the four for interview rooms 1, 2, 3, and 4, respectively. But secretary assigns them to the four rooms in a complete random model. We have to find the probability that all four ends up in the correct room and none of them ends up in the correct room. Step 2 : a) Here it is given that secretary arranged them randomly. So the possible ways that 4 people can be arranged in 4 rooms = 4! = 24 ways We have to find the probability that all ends up in correct order. Since there only one way to arrange everyone in the correct order= ABCD respectively So P( all four ends up in the correct room) = 1/24