Question

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

Answer 1

Answer:

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 = $3nCn$

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 = $3(nC2) + 2nC1$

d) in which all 3 students are in different classes

Each student 1 is selected from each class of n students

So $3(nC1) = 3n$