Estimating size of state space search problem
So lets take an 8 queens problem. Intially the size of state is 64C8 where 64 is the number of squares in a chess board and 8 is the number of queens that can be placed.
Now lets say, you can only put one queen in each column so that's only 8 squares available. This reduces the branching factor from 64 to 8. Now the size of state is 8C8 only.
Now lets say, you can only use 2 queens instead of 8. This reduced the depth from 8 to 2. So in this case instead of being 8 queens , now it's going to be a 2 queens problem. So that changes the size of state from 8C8 to 8C2. Cheers man.