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CAT 2019 Quant Question with Solution 11

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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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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