Answer:
There are a total of 210 different four-person teams that could be chosen.
Step-by-step explanation:
In order to calculate the greatest number of different four-person teams we need to calculate the combination of 10 people taken four by four as shown below:
[tex]C_{10,4} = \frac{10!}{4!(10 - 4)!}\\C_{10,4} = \frac{10!}{4!*6!}\\C_{10,4} = \frac{10*9*8*7*6!}{4!*6!}\\C_{10,4} = \frac{10*9*8*7}{4*3*2}\\C_{10,4} = \frac{5040}{24} = 210[/tex]
There are a total of 210 different four-person teams that could be chosen.
