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The planning committee at school has 10 members. Exactly four of these members are teachers. A four-person subcommittee with at least one member who is a teacher must be formed from the members of the planning committee. How many distinct subcommittees are possible?

 Apr 13, 2021
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Because there are 5 teachers on the committee, there are 6 non-teachers. Now, in total, we can form (11 \choose 4) = 330 subcomittees. The number of subcommittees with zero non-teachers is the number of subcommittees formed by the 5 teachers, totaling (5 \choose 4) = 5. So, the number of subcomittees with at least one non-teacher is 330 - 5 = 325

 

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 Apr 13, 2021

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