You would probably help the student much more if you gave him a few well directed hints rather than just solving his homework for him. It is much more helpful to say something such as:
Always attempt to break a big problems down into smaller steps: 1) Try to determine how many ways you can put 5 of those 12 students into the first room. 2) After that, determine how many ways you can put 4 of the remaining students into the second room. 3) Then determine how many ways you can put 3 of the final remaining students into the last room. 4) The answer is pretty easy after you've done those three calculations.
With hints, the student still needs to go through some of the work and hence through some of the learning process.
N. Silver wrote in message
E. Sanchez wrote:
> Twelve students are in the class, they are split > so that five go to room A, four to room B, > and three to room C. How many different ways > can this Happen?
12 Choose 5, and then 7 Choose 4 (and then 3 Choose 3).