SOLUTION: Mrs. Smith has twenty children in her class. In how many ways can she choose 4 members and a captain to form a quiz team?

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Question 356904: Mrs. Smith has twenty children in her class. In how many ways can she choose 4 members and a captain to form a quiz team?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is easier if you consider the problem in two steps:
1. Pick a team of 5 members
2. From the members of that team, pick a captain.

For picking a team, this is a problem of figuring out how many sets of 5 are possible when picking from a group of 20. This is a combination which we can find using:
%2820%2A19%2A18%2A17%2A16%29%2F%281%2A2%2A3%2A4%2A5%29
The 4*5 cancels the 20 and the 2*3 (or 6) cancels with the 18 (leaving 3):
19*3*17*16 = 15504
So there are 15504 possible teams of 5 which can be formed from the 20 children.

Now we can pick the captain. On each of these 15504 teams, there are 5 possible choices for captain. So there are 15504*5 = 77520 possible ways of picking a team of 5 with one of the five being captain.