Introduction:
In this question, we need to find out the number of ways in which 12 students can be equally divided into three groups.

Solution:
To divide 12 students into three groups, we need to follow the steps given below:

Step 1: First, we need to find out the size of each group. As we need to divide 12 students into three groups, the size of each group will be 12/3 = 4.

Step 2: Now, we need to select 4 students from 12 for the first group. This can be done in 12C4 ways.

Step 3: After selecting 4 students for the first group, we need to select 4 students from the remaining 8 for the second group. This can be done in 8C4 ways.

Step 4: Now, the remaining 4 students will form the third group.

Step 5: As the order in which we select the students for each group does not matter, we need to divide the total number of ways obtained in Step 2 and Step 3 by 2! (the number of ways to arrange the groups).

Step 6: The total number of ways in which 12 students can be equally divided into three groups is given by:

12C4 × 8C4 / 2! = (495 × 70) / 2 = 17325

Therefore, the number of ways in which 12 students can be equally divided into three groups is 17325.

Conclusion:
In conclusion, the number of ways in which 12 students can be equally divided into three groups is 17325. The solution involves finding the size of each group, selecting students for each group, and taking into account the order in which the groups are arranged.