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Chapter 1: Q. 1.22 (page 16)

In Problem 21, how many different paths are there from A to B that go through the point circled in the following lattice?

Short Answer

Expert verified

The total number of paths from A to B is18.

Step by step solution

01

Step 1. Given information.

To go from point A to B, a person has to go one step up or one step to the right at each move. To reach point B through the circled point, there are two paths - One is from A to the circled point and the other is from circled point to B.

02

Step 2. Find the number of paths.

Let the circled point be C

No. of ways to reach from A to C is 2, which are right then up then right then up or up then right then up then right.

So, number of paths from A to C =4!2!2!=4×3×2!2×1×2!=6

No. of paths from C to B = 3(2steps right and 1step up)

Therefore, total number of paths from A to B =6×3=18.

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