<p>Find the total number of ways of answering five objective type questions, each question having four choices.</p>
Step-by-Step Solution
Key Concept: Each question is independent with 4 choices available. Since we must answer all 5 questions and each has 4 distinct options, we apply the fundamental counting principle by multiplying choices across all questions.
<p><strong>Step 1:</strong> Identify the structure - We have 5 independent questions, each with 4 mutually exclusive choices.</p><p><strong>Step 2:</strong> Apply fundamental counting principle - For each question, there are 4 ways to answer.</p><p><strong>Step 3:</strong> Since questions are independent (answering Q1 doesn't restrict Q2's options), multiply the number of choices:</p><p>Total ways = 4 × 4 × 4 × 4 × 4 = 4<sup>5</sup> = 1024</p><p><strong>Insight:</strong> This is a classic application of the multiplication rule where we have 5 sequential tasks (answering each question), each with 4 independent options.</p><p>∴ Answer: <strong>4<sup>5</sup></strong></p>
Correct Answer: 4^5