Question 31.
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
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Question Explanation
Text ExplanationVideo Explanation
The number of paths from (1, 1) to (8, 10) via (4, 6) = The number of paths from (1,1) to (4,6) * The number of paths from (4,6) to (8,10)
To calculate the number of paths from (1,1) to (4,6), 4-1 =3 steps in x-directions and 6-1=5 steps in y direction
Hence the number of paths from (1,1) to (4,6) = = 56
To calculate the number of paths from (4,6) to (8,10), 8-4 =4 steps in x-directions and 10-6=4 steps in y direction
Hence the number of paths from (4,6) to (8,10) = = 70
The number of paths from (1, 1) to (8, 10) via (4, 6) = 56*70=3920
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