If Ms. Murphy has to select 4 swimmers from 9 swimmers, then she should use the formula:
[tex] A_n^k=\dfrac{n!}{(n-k)!}, [/tex] 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
[tex] 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. [/tex]
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.
