Permutations & Combinations
Fundamental Principle of Counting
Grade 11
Question:
<p>There are three stations A, B and C, five routes for going from station A to station B and four routes for going from station B to station C. Find the number of different ways through which a person can go from A to C via B.</p>
Step-by-Step Solution
Key Concept: When traveling through intermediate points, multiply the number of routes at each stage to find the total number of paths.
<p><strong>Step 1:</strong> There are 5 routes from station A to station B.</p><p><strong>Step 2:</strong> There are 4 routes from station B to station C.</p><p><strong>Step 3:</strong> To go from A to C via B, the person must first go from A to B and then from B to C.</p><p><strong>Step 4:</strong> By the Fundamental Principle of Multiplication, total number of different ways = 5 × 4 = 20 ways.</p>
Correct Answer: 20