Question

The below grid represents the map of your neighborhood. Your home is at the corner labeled A, while your work is at the corner labeled B. The corner marked with is your favorite coffee shop. (a) How many different paths of minimal length are there from your home to your work? b) How many different paths of minimal length are there from your home to your work that let you stop at your favorite coffee shop?

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Answer #1

a)

Number of paths =n

Number of ways to have 5 east and 4 steps north

Then n=9!/(5!*4!)=126

B)

Number of paths=N

4steps to east and 1 step to coffee shop*N(1 step east and 3 stops North to point B)=(5!/(4!*1!))*(4!/(1!*3!))=5*4=20

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