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 are possible?

b. how many choices are 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?

Step-by-step explanation:

Given that there are three classes, each consisting of n students. From this group of 3n students, a group of 3 students is to be chosen.

a) Out of 3n students to draw 3 students we use combination since order does not matter.

Hence no of ways =

b) If three students are to be in same class, either from I class or Ii or III

No of ways = nC3 + nc3+nc3 = 3(nC3)

c) 2 of the 3 students are in the same class and the other student is in a different class.

2 can be either from I or II or III and the remaining from any one of other classes.

So no of ways =

d) in which all 3 students are in different classes

Each student 1 is selected from each class of n students

So