On the street grid shown, a courier moves only east (right) or north (up) from A to B. How many shortest routes start with a step to the east?

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Accepted Answer

10. A shortest route needs 3 E and 3 N steps. After the first E, the remaining 2 E and 3 N can be ordered in ^5C_2=10 ways. (20 counts all shortest routes.)

On the street grid shown, a courier moves only east (right) or north (up) from A to B. How many shortest routes start with a step to the east?

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