When doing the problem I got a value of 3.27 x 10^6. I\'m not sure if I did it p

Question

When doing the problem I got a value of 3.27 x 10^6. I'm not sure if I did it properly, since my value seems high. I just need verification since I was not able to find the problem anywhere online. I don't want simply a yes or no. Show your work please.

Consider an ant that is walking on a Cartesian grid, starting at (0,0) and ending at (10, 15). The ant

always chooses to walk exactly one unit either up or to the right (towards his destination) whenever he

arrives at a Lattice point. (A Lattice point is a point with integer coordinates.) Thus, from (0,0) he either

walks to (1, 0) or (0, 1). How many different paths can he take on his walk?

Explanation / Answer

Your answer is correct.

The number of different paths is equal to (10+15)! / ((10!)*(15!)).

Proof:

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