12C4×8C4×4C4÷3! = 5775 there three groups that's why it is divisible by 3!

Introduction:
The problem requires us to find the number of ways in which 12 students can be equally divided into three groups. In other words, we need to find the number of ways in which we can distribute 12 students among three groups such that each group has an equal number of students.

Method:
In order to solve this problem, we can use the concept of combinations. We need to divide the 12 students into three groups of 4 students each. We can choose 4 students from the total of 12 students in C(12,4) ways for the first group. For the second group, we can choose 4 students from the remaining 8 students in C(8,4) ways. Finally, the remaining 4 students form the third group. Therefore, the total number of ways in which 12 students can be equally divided into three groups is given by:

C(12,4) x C(8,4) = (12! / (4! x 8!)) x (8! / (4! x 4!)) = (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1) x (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 495 x 70 = 34650

Therefore, there are 34650 ways in which 12 students can be equally divided into three groups.

Conclusion:
In conclusion, the problem of dividing 12 students equally into three groups can be solved using the concept of combinations. The total number of ways in which this can be done is 34650.