Answer to Question #325045 in Statistics and Probability for Akib

Question

If a multiple-choice test consists of 5 questions,

each with 4 possible answers of which only 1 is correct,

(a) in how many different ways can a student check off

one answer to each question?

(b) in how many ways can a student check off one

answer to each question and get all the answers

wrong?

Answer 1

(a) The number of ways a student can check off each question is 4. The total number of ways he can check off all the questions:

$N=4\cdot4\cdot4\cdot4\cdot4=4^5=1024.$

(b) The number of ways a student can give an incorrect answer to each question is 3. The total number of ways he can check off one answer to each question and get all the answers wrong:

$M=3^5=243.$