You are given ten toy blocks and want to build stairs going to a wall, with each level of the staircase being a solid color
4 Blue blocks on the bottom,
3 Green blocks next,
2 Orange blocks next, and
1 Red block on top
But there is a catch. The floor slants toward the wall and the blocks are made of superslickium. So if a blue block is put on the floor, it will slide until it is stopped by the wall or another block that is stopped by the wall. Similarly, if a green block is placed on a blue block, it will slide toward the wall until stopped by the wall or another green block.
Looking at the order you place the blocks, how many ways are there for building this staircase?
You could build by levels: BBBBGGGOOR
or you could build by columns: BGORBGOBGB
or BBGBGOBGOR, etc.
How many possibilities?