<p>In a class, there are 15 boys and 10 girls. How many ways a teacher can select 1 boy and 1 girl to represent the class at a seminar?</p>
Step-by-Step Solution
Key Concept: Use the fundamental counting principle: when selecting independent items from different groups, multiply the number of choices for each group. Here, selecting 1 boy AND 1 girl means we multiply the ways to select each.
<p><strong>Step 1:</strong> Identify the requirement: Select 1 boy AND 1 girl (two independent selections)</p><p><strong>Step 2:</strong> Find ways to select 1 boy from 15: C(15,1) = 15 ways</p><p><strong>Step 3:</strong> Find ways to select 1 girl from 10: C(10,1) = 10 ways</p><p><strong>Step 4:</strong> Apply Fundamental Counting Principle: Total ways = 15 × 10 = 150</p><p><strong>Reasoning:</strong> For each boy selected (15 choices), there are 10 independent choices for the girl, giving 15 × 10 combinations.</p><p>∴ Answer: <strong>150</strong></p>
Correct Answer: 150