Question

2. 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. ​

Answer 1

If the committee must consist at least one student, the probability is 99.96%

Explanation:

Given;

number of teachers = 5

number of students = 20

Total number of committee members = 25

Possible outcome of all the members in the 4 committee = 25C₄ ways

= 12650

If the committee must consist at least one student, then the possible outcome;

= Total possible outcome - committee with no student

= 25C₄ ways - 5C₄ ways (all committee members are teachers)

= 12650 - 5

= 12645

The probability that the committee will consist at least one student;

= 12645 / 12650

= 0.9996

= 99.96%

Therefore, if the committee must consist at least one student, the probability is 99.96%