Consider the following counting problem. At a school there are 19 seniors. Of the 19, a team of 4 will be randomly selected to represent the school. Of the 4 the first will be a spokesperson, the second will write the script, the third will produce and the fourth will run the camera. How many ways can the students be selected to fill the 4 different positions?

Question

Consider the following counting problem. At a school there are 19 seniors. Of the 19, a team of 4 will be randomly selected to represent the school. Of the 4 the first will be a spokesperson, the second will write the script, the third will produce and the fourth will run the camera.  How many ways can the students be selected to fill the 4 different positions?

anonymous · Answer

Order matters: the number of ways is then ${}_{19}P_{4}=\dfrac{19!}{(19-4)!}$.