Question

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 13 candidates qualified for all three of the positions. Determine the number of different ways the positions can be filled by these applicants.

Answer 1

Answer:

There are 1716 ways the three positions can be filled by these applicants.

Step-by-step explanation:

Permutation is the number of arrangement of k items from n distinct items.

$^{n}P_{k}=\frac{n!}{(n-k)!}$

For example, permutation can be used to compute the number of ways to arrange 4 mathematics books together when arranging all the 7 books on a shelf.

In this case there are 3 available nursing positions to be filled.

A total of 13 candidates are qualified for all the three positions.

Then the number of ways the 3 positions can be filled by the 13 candidates can be determine using permutation.

Compute the possible number of selections as follows:

$^{13}P_{3}=\frac{13!}{(13-3)!}=\frac{13!}{10!}=\frac{13\times 12\times 11\times 10!}{10!}=1716$

Thus, there are 1716 ways the three positions can be filled by these applicants.