Quantitative Aptitude – Principles of Counting – Number of Paths – With rectangular axes of coordinates

Slot – 1 – Quantitative Aptitude – Principles of Counting – Number of Paths – With rectangular axes of coordinates

With rectangular axes of coordinates – Video

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Q. 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?

Answer: 3920

Solution: dimension of rectangle with ends of diagonal being(1,1) and (4,6) = 3*5
thus number of paths from (1,1) to (4,6) = (5+3)!/5!3! =56
dimension of rectangle with ends of diagonal being(8,10) and (4,6) = 4*4
thus number of paths from (4,6) to (8,10) = (4+4)!/4!4! =70
so total number of paths from (1,1) to (8,10) via (4,6) = 56*70 =3920

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