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a school is 4 blocks east and 4 blocks south of a student's home, how many...

a school is 4 blocks east and 4 blocks south of a student's home, how many different street routes get him to school

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Answer #1

If your grid is such that you need to make 4 left and 4 down movements, then what you are looking at is in how many ways can you arrange the letters "LLLLDDDD". This is the same as asking how many ways can we place 4 L's in 8 slots. This is exactly what is counted by the binomial coefficient (8C4)=70

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