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?

865

Step-by-step explanation: The set of possibilities are:

Subcommittee is of 4 people according to:

4 teachers 0 other member total possibilities 1

3 teachers 1 teachers C₄,₃ = 4 and other member 6 6*4 = 24

2 teachers 2 C₄,₂ = 4!/2! = 12 2 (om) and C₆,₂ = 6!/4! = 30

30*12 = 360

1 teacher 3 (om) 4 and C₆,₃ = 6!/3! = 120

120*4 = 480

Total ways of committee 1 + 24 + 360 + 480 = 865