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I live 9 (rectangular) blocks from Tech, and I walk each morning. The trip is 3...

I live 9 (rectangular) blocks from Tech, and I walk each morning. The trip is 3 blocks north and 6 blocks west; and I have to follow the streets, so I cannot cut diagonally.

At each intersection, I must choose whether to walk north or walk west. Thus, I must make 9 choices of which to take, but of course must go north 3 times and west 6 times.

How many possible complete trips to Tech are there?

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Answer #1

Sol: Here, at each intersection , he has the option to travel either west or north, provided he takes 3 norths and 6 wests of the 9 intersections. So, the no. of ways this trip to tech can be comoletco is equal to the number of ways in which we can select 3 out of 9 and the guy moves north in these 3 intersections and west in the rest 6. So, the no. of ways is 9C3=9*8*7/3*2=84

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