Question

Consider a three-dimensional grid whose dimensions are 10 by 15 by 20. you are at the front lower left corner of the grid and wish to get to the back upper right corner 45 "blocks" away. how many different routes are there in which you walk exactly 45 blocks?

Answer 1

 45 steps there will be 10 steps to the right then 15 steps up and 20 steps forward. It is just like counting sequences of 45 letters. so 10 is R  then 15  U, is and 20 is  F.  ending the multinomial coefficient

 (      45    )
 10, 15, 20 = 45/101520  or 45 over 10 15 20