Problem
COM-B1-M10-P004 Path \((0,0)\to(2,3)\)
#4
★☆☆☆☆ Level 1 of 5
How many shortest paths go from \((0,0)\) to \((2,3)\), if only right and up moves are allowed?
There are \(5\) steps: choose positions for the two right moves.
One must make \(2\) right moves and \(3\) up moves. There are \(5\) steps total, so choose positions for the \(2\) right moves: \(\binom{5}{2}=10\).
Connection between paths and combinations.