Quantitative Aptitude – Modern Math – Geometry

Slot – 1 – Quantitative Aptitude – Modern Math – Geometry – With rectangular axes of coordinates

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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