SOLUTION: In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 20 prospective jurors?

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Question 938036: In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 20 prospective jurors?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The way I see it, choosing the 12%2B2=14 people who could form the final panel is the same as choosing the 20-14=6 people that are not wanted.
That is 20%2A19%2A18%2A17%2A16%2A15%2F%281%2A2%2A3%2A4%2A5%2A6%29=19%2A17%2A15%2A8=38760 ,
so there are 38760 different sets of 14 people that can be picked.
For each of those 14 sets, there are
14%2A13%2F%281%2A2%29=7%2A13=91 possible sets of 2 alternates.
That gives us 38760%2A91=highlight%283527160%29 possible panels that can be formed.

Another way:
Out of the 20 people available, there are
20%21%2F%288%2112%21%29=125970 ways to chose the 12 jurors,
and in each case, from the 20-12=8 people remaining, there are
8%2A7%2F%281%2A2%29=4%2A7=28 ways to choose two alternates.
So, there are 125970%2A28=highlight%283527160%29 possible panels that can be formed.