There are 5775 ways to divide the 12 students into 3 groups of 4 for training workshops, considering the composition of each group but not their order.
To find the number of ways to divide 12 students into 3 groups of 4 for training workshops, we need to consider the order of the students within each group and the order of the groups themselves.
Here's how to approach this:
1. Combinations for each group:
We need to choose 4 students out of 12 for each group. This can be done in 12C4 ways for each group.
- To calculate 12C4, you can use the formula: n! / (r! * (n-r)!)
Therefore, for each group, there are 12! / (4! * 8!) = 495 ways to choose the students.
2. Considering group order:
If the order of the groups doesn't matter (only the composition of each group), we need to divide the total number of combinations by the number of ways to order 3 groups.
There are 3! (3 factorial) ways to order 3 groups.
3. Final calculation:
Therefore, the total number of ways to divide the students into 3 groups of 4, considering the order of students within each group but not the order of the groups themselves, is:
Total Combinations = 3 * (495)^3 = 5775