Question 1210219
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If every move is either down or to the right, then obviously the path can't pass through any point more than once....<br>
So to get from A to B we need to move, in some order, 3 steps to the right and 3 units down.<br>
Represent a move to the right as "R" and a move down as "D".  Then each distinct path is represented by a string of 3 "R"s and 3 "D"s.  By a common counting principle, the number of ways of arranging the symbols "RRRDDD" is<br>
{{{6!/((3!)(3!))=20}}}<br>
ANSWER: 20<br>