Consider the (nx n)-grid (drawn below in the case n = 6). How many distinct walks are there from the bottom left corner to the top right corner, if you are only allowed to go up or to the right? How many distinct walks are there in a 3-dimensional (nx nx n)- grid from the bottom left front corner to the top right back corner, if you are only allowed to go up, right, or to the back? Show all your working and justify you answers.

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