Hi.
Let's say that we have two boxes of pencils (in first box just blue and in second just red pencils). So the question now is, in how many ways can we put x red and y blue pencils in the line?
Example: we have 3 Red pencils, and 1 Blue. Then we have 4 different ways. Combinations: BRRR, RBRR, RRBR, RRRB.
So with 10 Red and 10 Blue pencils we have 184756 different ways of putting them in line. So guys, how to write this in a recursive way?
Thank you very much for your help.
This sounds like homework, so here are some hints:
When dealing with recursion, you need to think about the base case. Here this base case is 0 pencils. How many ways can you order 0 pencils?
Ok, now the recursive cases: how many ways can you order a non-zero amount of pencils? If you have any red pencils then you can start with a red pencil, followed by the rest of the pencils. If you have any blue pencils then you can start with a blue pencil, followed by the rest of the pencils.
Think binary tree, depth = # of pencils in the line.
The root is zero pencils. Level 1 had one blue pencil and one red pencil. Level 2....you see the pattern.
there is no need to do it in recursion form since it can be calculated using (x+y)!/(x!y!) but if u're insistent u can use something like this: C(x,y)=C(x-1,y)+C(x,y-1) with base cases: C(z,0)=C(0,z)=1 that z is any natural number ;)