Question 848552: There are three teachers and eight students on the student council. How many ways can a committee of 4 people be chosen if there must be at least one teacher on it?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! This can be achieved by:
(3 students, 1 teacher) (2 students, 2 teachers) (1 student, 3 teachers)
(8 choose 3)(3 choose 1) + (8 choose 2)(3 choose 2) + (8 choose 1)(3 choose 3) = 260
Alternative method. There are (11 choose 4) total ways to order. The only scenario left out is [4 students, 0 teachers] (note we cannot have 0 students, 4 teachers).
So (11 choose 4) - (8 choose 4)(3 choose 0) = 260
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