There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 16 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants. Step 1 There are three different positions that must be filled, and there are 16 possible candidates that can fill the positions. We need to count the number of ways to pick 3 of the 16 candidates. Recall there are two ways to count the number of ways to choose r of n objects: permutations and combinations. For permutations, the order the items are selected matters, but for combinations the order does not matter. Consider the following situations. Situation 1: Candidate A gets position 1, Candidate B gets position 2, and Candidate C gets position 3 Situation 2: Candidate A gets position 3, Candidate B gets position 2, and Candidate C gets position 1. The same three candidates have been selected, but the positions they fill are different. This indicates that the order of selection mattersmatters. So, we should use permutationspermutations to count. Step 2 Recall the Counting Rule for Permutations; the number of ways to arrange in order n distinct objects, taking n! them r at a time, is Pa,--y, where n and r are whole numbers and n2r. n(n - r)! The total number of nurse candidates is 16 and the number of positions to fill is 3. Using the formula to compute P16,3, substitute 16 simplify. for n and 3 for r, and 16! n! X3! 16! X!