- #1

- 256

- 18

"A boy begins walking from his starting point. Each hour, he either walks one kilometer to the east or one kilometer to the north, but he never walks in the same direction.

In how many different ways can he get to a point that is 8 kilometers to the north and 8 kilometers to the east of his starting point?"

The answer is 2^8, or 256. But shouldn't it be 2?

He can either start by going east, then north, then east - until his displacement is 8 km N, 8 km E

or he can start by going north, then east, then north, etc

So shouldn't it be 2? Can someone break this down for me if I am wrong?