03 In a class of 12 students 7 are good and 5 are evil If on

03 In a class of 12 students, 7 are good and 5 are evil. If one selects at random a team of 3 students from the class, what is the chance that the team contains some good student?

Solution

If a team of 3 student is selected then, we can have one good, two good students or all the three good students then, we can say, we have some good students in the team.

No. ways of getting one good student=C(7, 1)*C(5, 2)

No. ways of getting two good students=C(7, 2)*C(5, 1)

No. ways of getting three good students=C(7, 3)*C(5, 0)

Therefore, the no, of ways of getting some good students in the team

=C(7, 1)*C(5, 2)+C(7, 2)*C(5, 1)+C(7, 3)*C(5, 0)

=7*10+21*5+35

=210

The total number of ways of selecting 3 students form the class=C(12, 3)=220

therefore, the chance that the team contains some good student=210/220=21/22