A teacher-student committee consisting of 4 people is to be formed from 5 teachers and 20 students. Find the probability that the committee will consist of at least one student.
Answers
Given : A teacher-student committee consisting of 4 people is to be formed from 5 teachers and 20 students
To Find : probability that the committee will consist of at least one student
Solution:
Teachers 5
Students = 20
Total = 25
committee consisting of 4 people
4 people out of 25 can be selected in ²⁵C₄ ways
= 12650
committee will consist of at least one student
= Total - committee will not consist of any students
= 12650 - ⁵C₄ ( all 4 be teachers from 5 teachers)
= 12650 - 5
= 12645
probability that the committee will consist of at least one student = 12645 / 12650
= 99.96 %
99.96 % is the probability that the committee will consist of at least one student
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