Question

A professor in a graduate course wants to form a team of three students to represent the class at a national case competition? Of the 20 students in the class, 5 have undergraduate degrees in Economics, 9 in Engineering and 6 in business. If the team is formed at random, what is the probability that there will be at least two students with different undergraduate majors on the team?

Answer 1

A professor in a graduate course wants to form a team of three students to represent the class at a national case competition. There are 20 students in the class, 5 have undergraduate degrees in Economics, 9 in Engineering and 6 in business.

We want to find the probability that there will be at least two students with different undergraduate majors on the team.

Now from 20 students 3 students can be chosen in = 1140 ways.

Now we consider the cases which are favorable to our event i.e. at least two students from different undergraduate majors subject on the team.

So the required probability is given by,

( Total number of favorable ways / total no of ways )

=(1026/1140) =0.9

Note:- at least 2 students from different undergraduate mejors subject means, 2 students from any one subject and 1 students from other than these subject or from each subject one student can be chosen. Suppose we take the 1st case i e. from economics 2 students can be chosen and from engineering 1 student can be chosen. Now from 5 students, 2 students can be chosen in ways and from 9 students, 1 student can be chosen in ways. Similarly we get next all the cases.