This is probably amongst the tougher questions in the CAT 2019 question paper. It uses a variety of concepts including coordinate geometry and arrangements. All **CAT previous year paper** have these kind of questions that are extremely tough. While the **CAT syllabus** will probably classify this under arrangements, only practice will help you identify that there are multiple layers to the problem. Identifying these questions can come only with practice that you do as a part of your online **CAT Preparation**

Question 3 : 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 [TITA]

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Let us first consider travelling from (1,1) to (4, 6)

This means, Travelling from 1 to 4 units in the x axis -> 3 horizontal movements (h h h)

And travelling from 1 to 6 units in the y axis -> 5 vertical movements (v v v v v)

No matter how we proceed, reaching from (1,1) to (4,6) requires 5 vertical movements and 3 horizontal movements.

So, Number of paths to travel from (1,1) to (4,6) = Number of ways of arranging (h h h v v v v v)

Number of ways of arranging (h h h v v v v v) =

Similarly, travelling from (4, 6) to (8, 10) requires 4 horizontal movements and 4 vertical movements

Number of ways of arranging (h h h h v v v v) =

Total number of paths = x = x = 3920

The question is **"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 [TITA] " **

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