Math Problem Statement
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
Solution
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:
-
Direct paths from City M to City O:
- There are 5 direct paths from City M to City O.
-
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:
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:
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:
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Path Counting
Basic Multiplication
Formulas
Number of paths = direct paths + paths via another city
Theorems
Addition principle of counting
Suitable Grade Level
Grades 6-8