posted by Martha
You have 48 yellow blocks and 40 green blocks. What is the greatest number of identical towers that you can build using all 88 blocks?
For a particular tower built, all 48 yellow blocks can be rearranged in 48! ways, and similarly, the 40 green blocks can be arranged in 40! different ways.
So the number of identical towers that can be built is 48!*40! This is approximately equal to 1.0*10^19.
However, if the number of different towers is required, the number is 88! if all blocks are of different colours. Since we have found 48!*40! identical towers for each tower that we build, so there are 88!/(40!48!) different towers using the above 88 blocks. This evaluates to "only" 18312575054317505569702710 different towers, or 1.8*10^25 different towers.
You can just build as many identical towers as you're little heart can handle, and don't you let nobody tell you otherwise honey.