Question:
With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is
Correct Answer: 3920
Let A, B and C represent the coordinates (1, 1), (8,10) and (4,6) respectively.
The number of ways to go from A to B via C = (The number of ways to go from A to C)×(The number of ways to go from C to B)
$={}^{8}{{C}_{5}}\times {}^{8}{{C}_{4}}=3920$
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