The Professor's Response
A bag contains 50 names in it. A professor plans to draw three names from the bag to win a free
graphing calculator. How many different sets of three winners can be drawn from the bag?
See the professor's answer below.
Since the problem asks, "How many different sets...," it is a counting question. We should first check to see if the problem is a combination couting problem: 1) Are we counting the number of possible subsets? Yes, we are taking 3 names from a set of 50. 2) Does the order of the names matter once they are drawn? No, we do not need to pay attention to order here because if Jimmy, Maria, and Penny are selected, it is the same as saying Maria, Penny, and Jimmy were selected. Nothing will change. They are each getting a calculator. The same calculator. If they were being assigned to different prizes, then the same three people could be given different prizes in different scenarios. Then order would matter. 3) Are the selections without replacement? It doesn't say so, but we can assume the prof wants to give three different students the prize, which would not allow one person to be chosen twice. We can assume the selections are without replacement. This meets the criteria for a combinations problem, so we do 50C3. This can be done in the calculator or using the formula: 50!/[47!(3!)]