Forming a committee
Probability
Level
2
In how many ways can a committee of 5 be formed from a group of 11 people consisting of 4 teachers and 7 students the committee must include at least 3 teachers?
The answer is 91.
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1 solution
we have 2 choices : first having 3 teachers in the committee in 4 ways then choose 2 student in 21 ways by multiple principle we have 4*21 ways . In our second choice we choose all 4 teachers by 1 choice and then we need 1 student that we can choose by 7 ways and by multiple principle we have 7 ways . Finally by addition principle we have 7+84 =91 ways...