Question

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?

Answer 1

Answer:

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