Math CentralQuandaries & Queries


Question from Christopher:

math team has 20 people on the team but only 4 can enter the competition. The team captain has to pick 4 of them but he knows that he cannot put James, Bill or Todd on the team with one another or there will be problems. what would the formula be to find the solution to how many possible team combinations the are

Hi Christopher,

Suppose he puts James on the team, then he has 3 more team members to pick and he only has 17 choices since he can't pick Bill or Todd. How many ways are there for choosing 3 people from 17? There are the same number of teams with Bill on the team and the same number with Todd on the team.

All that remains are the teams without James, bill or Todd. How many ways are there to choose a team of 4 members from 17 people?

I hope this helps,

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