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Counting and Basic Probability · Question 12 of 65

Question 12

MediumOriginal question

A quiz has 5 questions, and each question has 4 answer choices. A student marks exactly one choice for every question. In how many different ways can the answer sheet be filled?

Options for question 12

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Each question is answered in 4 ways, independently of the others.

  2. Ways =4×4×4×4×4=45=1024= 4 \times 4 \times 4 \times 4 \times 4 = 4^5 = 1024.

Worth noting

625 is 545^4: the base must be the number of choices per question (4), raised to the number of questions (5). 20 multiplies 5 by 4 once.

Concept
Repeated independent choices give a power
Typical time
70 s
Your time
—
The rule this testsThe counting principle
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