Multiple choice

In an examination there are three multiple choice questions and each question has $4$ choices out of which only one is correct. If all the questions are compulsory, then number of ways in which a student can fail to get all answers correct, is

  1. $11$
  2. $12$
  3. $27$
  4. $63$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Each of the 3 questions has 4 choices, giving a total of 4 * 4 * 4 = 64 possible ways to answer. Since there is only 1 way to get all answers correct, the number of ways to fail to get all answers correct is 64 - 1 = 63.

AI explanation

By the fundamental principle of counting, there are 4 choices for each of the 3 questions, yielding 4 times 4 times 4 equals 64 total possible ways to answer. Since only 1 combination yields all correct answers, the remaining 64 minus 1 equals 63 combinations represent the ways to fail to get all answers correct.

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