/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 1.22 In Problem 21, how many differen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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脳3脳2!2脳1脳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脳3=18.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices are possible if

(a) both books are to be on the same subject?

(b) the books are to be on different subjects?

Determine the number of vectors(x1,...xn) such that each xiis either 0or 1and

鈭�i=1nxi鈮�k

Argue that there are exactly rkn-1n-r+ksolutions of x1+x2+路路路+xr=nfor which exactly kof the xiare equal to 0.

In how many ways can nidentical balls be distributed into rurns so that the ithurn contains at least miballs, for each i=1,...,r? Assume that n鈮�鈭�i=1rmi.

Present a combinatorial explanation of why

nr=nr,n-r
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.