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Chapter 1: Q. 1.21 (page 16)

Consider the grid of points shown at the top of the next column. Suppose that, starting at the point labelled A, you can go one step up or one step to the right at each move. This procedure is continued until the point labelled B is reached. How many different paths from A to B are possible? Hint: Note that to reach B from A, you must take 4steps to the right and 3steps upward.

Short Answer

Expert verified

The possible number of paths from A to B is35.

Step by step solution

01

Step 1. Given information.

It is given that to reach B from A, 4steps are to be taken to the right and 3steps up. So, total 7 steps are to be taken.

02

Step 2. Find the possible number of paths.

Using multinomial rule, the possible number of paths from A to B is given by m!n1!n2!

where,

m=Total number of steps =7

n1=Total number of steps taken to the right =4

n2=Total number of upward steps =3

Therefore, the possible number of paths from A to B=7!4!3!=7脳6脳5脳4!3脳2脳1脳4!=35

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