Question

Ms. Murphy has to select 4 swimmers out of 9 swimmers to create a relay team. In how many ways can she create a relay team? 3,024 6,561 15,120 362,856

Answer 1

If Ms. Murphy has to select 4 swimmers from 9 swimmers, then she should use the formula:

$A_n^k=\dfrac{n!}{(n-k)!},$ where n is the number of all objects and k is a number of selected objects.

In your case, n=9 and k=4, then

$A_9^4=\dfrac{9!}{(9-4)!}=\dfrac{9!}{5!}=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9}{5!}=6\cdot 7\cdot 8\cdot 9=3024.$

Answer:  she can create a relay team in 3024 ways.

Another way: Ms. Murphy can choose first swimmer in 9 ways (first from 9), then second in 8 ways (1 from 8), third in 7 ways and fourth in 6 ways. Using the product rule:

9·8·7·6=3024.

Answer 2

It would be nPr = n!/(n-r)! = 9!/(9-4)! = 9!/5! = 3024