Multiple choice

In how many ways can a student take a test consisting of 10 questions such that he answers at least two questions with each question having exactly one correct answer among four options given?

  1. 410 - 41

  2. 510 - 1

  3. 510 - 41

  4. 45 × 48
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

Each of the 10 questions has 5 possible outcomes since the student can choose any of the 4 given options or leave the question unattempted. The total number of ways to attempt the test without any restriction is 5^10. The number of ways the student answers fewer than two questions is the sum of answering zero questions and answering exactly one question, which equals 1 + 10 * 4. Subtracting these excluded cases from the total gives the required number of ways as 5^10 - (10 * 4 + 1), which simplifies to 5^10 - 41.

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