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How many ways are there to walk from $P$ to $Q$ by only taking steps to the right or up? 

 

[asy]

draw((0,0)--(2,0)--(2,6)--(6,6));
draw((0,0)--(0,3)--(6,3)--(6,6));

draw((0,1)--(2,1));
draw((0,2)--(2,2));
draw((1,0)--(1,3));
draw((3,6)--(3,3));
draw((4,6)--(4,3));
draw((5,6)--(5,3));
draw((2,4)--(6,4));
draw((2,5)--(6,5));

label("$P$",(0,0),SW);
label("$Q$",(6,6),NE);
[/asy]

 Feb 20, 2020
 #1
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0

There are C(6,3)*C(7,2) = 420 ways to get from P to Q.

 Feb 21, 2020

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