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Grid route count

CombinatoricsEasy

A courier walks on a grid of unit blocks from the corner $(0, 0)$ to the corner $(4, 3)$ . Each move goes $1$ block east or $1$ block north. How many different routes are there?

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Hint

A route is a sequence of moves; decide which of the moves go north.

Solution

Every route uses $4$ east moves and $3$ north moves, so $7$ moves in total.
A route is fixed by choosing which $3$ of the $7$ moves go north.
The number of routes is $(3 7) = 35$ .

Answer: $35$

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