Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

In a class of 20 students, all but 4 of the students put their names on a typed assignment. If the teacher randomly guesses, what is the probability that she correctly guesses which paper belongs to each of the four remaining students? Express your answer as a common fraction.
Solution
The probability that the teacher guesses the first student's paper correctly is . Given that the first guess is correct, the probability that she guesses the second student's paper correctly is . Given that both of the first two guesses were correct, the probability that she guesses the third student's paper correctly is . If the first three are correct, then the fourth will be correct with probability . The probability that all four guesses will be correct is .
Final answer
\frac{1}{24}