The path from city M to city N can be taken by 6 paths, from city M to city O can be taken by 5 paths, from city N or city O to city P can be taken by 5 paths, while city N to city O can only be taken by 1 path. How many paths are there from city M to city O....

a. 100 ways

b. 110 ways

c. 120 ways

d. 130 ways

To solve this, we need to count the number of possible paths from **City M** to **City O** through **City N** or directly.

Here’s the breakdown:

1. **Direct paths from City M to City O**:
   - There are **5 direct paths** from City M to City O.

2. **Paths from City M to City O via City N**:
   - First, there are **6 paths** from City M to City N.
   - From City N, there is **1 path** to City O.
   - Therefore, the number of ways to go from City M to City O via City N is:
     \[
     6 \times 1 = 6 \text{ paths}
     \]

### Total number of paths:
- **Direct paths** from City M to City O = 5
- **Paths via City N** = 6

Thus, the total number of paths from City M to City O is:
\[
5 + 6 = 11
\]

### Extending the paths from City M to City P:
Now we need to add the possibilities from City O or City N to City P. However, since the problem only asks about the number of paths from **City M to City O**, the correct answer is:

\[
\boxed{11}
\]



The path from city M to city N can be taken by 6 paths, from city M to city O can be taken by 5 paths, from city N or city O to city P can be taken by 5 paths, while city N to city O can only be taken by 1 path. How many paths are there from city M to city O?
a. 100 ways
b. 110 ways
c. 120 ways
d. 130 ways

This problem explores path counting concepts involving combinatorics. Learn how to determine the number of paths from City M to City O, considering both direct paths and paths via City N. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation