Problem 9STE

Consider three classes, each consisting of n students. From this group of 3n students, a group of 3 students is to be chosen.

(a) How many choices arc possible?

(b) How many choices arc there in which all 3 students are in the same class?

(c) How many choices are there in which 2 of the 3 students are in the same class and the other student is in a different class?

(d) How many choices are there in which all 3 students are in different classes?

(e) Using the results of parts (a) through (d), write a combinatorial identity.

Solution :

Step 1 of 5:

Given 3 classes, each consisting of n students.

Then from this group of 3n students, a group of 3 students is to be chosen.

a). From the given information we know that for the three classes, so each class consisting of n students.

Now we find the number of possible choices to a group of 3 students chosen from the group of 3n students in ways.