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

Given:  A committee consisting of 4 people to be formed from 5 teachers and 20 students.

To Find: Probability that committee will consist of at least one student.

Solution:

• Now we have given 5 teachers, 20 students and total are 25 people.

• So, the committee of 4 people formed will be:

              25 C 4  = 12650

• Now we have given that committee must have at least one student:

              = 12650 - committee (no students)

              = 12650  - 5 C 4  

              = 12650 - 5

              = 12645

• So, the probability that committee will have at least one student is:

              = 12645 / 12650

              = 2529 / 2530

Answer:

               Probability that committee will consist of at least one student is 2529 / 2530