Question

if a multiple choice test consit of 5 questions each with 4 possible answers of which only one is correct, (a) how many different ways can a student check off one answer to each question?
(B) how many ways can a student check off one answer to each question and get all the question wrong?

Answer 1

Answer on Question #65181 – Math – Statistics and Probability

Question

If a multiple choice test consist of 5 questions each with 4 possible answers of which only one is correct,

(a) How many different ways can a student check off one answer to each question?

(b) How many ways can a student check off one answer to each question and get all the questions wrong?

Solution

(a) For each question a student has 4 possible ways to check off. Then for 5 questions a student has $4^5 = 1024$ ways to check off answers.

(b) There are 3 wrong answers to each question. Then a student can choose wrong answer to the first question in 3 ways, to the second one in 3 ways and so on. So a student can check off one answer to each question and get all the questions wrong in $3^5 = 243$ ways.

Answer: (a) 1024; (b) 243.

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