# With rectangular axes of coordinates | Quantitative Aptitude – CAT Principles of Counting-Number of Paths

## CAT 2019 – Slot -1 - Question 1 - Number of Paths – With rectangular axes of coordinates

### Q. 1: 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

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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