Permutations & Combinations
Fundamental Principle of Counting
Grade 11
Question:
<p>There are 4 students for Physics, 6 students for Chemistry and 7 students for Mathematics gold medal. In how many ways can one of these gold medals be awarded?</p>
Step-by-Step Solution
Key Concept: When selecting from mutually exclusive categories, add the number of choices in each category to get the total number of ways.
<p><strong>Step 1:</strong> Physics gold medal can be awarded in 4 ways (to any of the 4 Physics students).</p><p><strong>Step 2:</strong> Chemistry gold medal can be awarded in 6 ways (to any of the 6 Chemistry students).</p><p><strong>Step 3:</strong> Mathematics gold medal can be awarded in 7 ways (to any of the 7 Mathematics students).</p><p><strong>Step 4:</strong> Since we need to award one of the three gold medals (the selections are mutually exclusive), by the Fundamental Principle of Addition, the total number of ways = 4 + 6 + 7 = 17 ways.</p>
Correct Answer: 17