Counting and Probability

Question

Suppose Fred randomly thinks of 5 whole numbers between 1 and 31 inclusive. What is the probability that George can correctly guess all 5 numbers?

???(Express as a fraction.)

Suppose Fred randomly thinks of 5 whole numbers between 1 and 31 inclusive. What is the probability that George can correctly guess all 5 numbers?

Answer 1

The number of ways of selecting 5 numbers from 31 numbers is 

 

₃₁C₅ = 31! / ( 26! * 5! ) = 169911  

 

George will only guess all 5 numbers correctly if his selection matches Fred's.  The probability of this occurring is 

 

1 / 169911