Question

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?

Answer 1

Answer:

We conclude that he have 84  possible complete trips to Tech.

Step-by-step explanation:

We know that he  live 9 (rectangular) blocks from Tech. The trip is 3 blocks north and 6 blocks west. We calculate number of  possible complete trips to Tech. We know that

$C^9_3=C^9_6$

We calculate

$C^9_{3}=\frac{9!}{3!(9-3)!}=\frac{9\cdot 8\cdot 7\cdot 6!}{3\cdot 2\cdot 1\cdot 6!} =84$

We conclude that he have 84  possible complete trips to Tech.