involving the construction of a number from a set of digits. Assume that 3 digits are selected at random from the set {2,3,6,7,9}{2,3,6,7,9} and are arranged in random order.

Question

involving the construction of a number from a set of digits. Assume that 3 digits are selected at random from the set {2,3,6,7,9}{2,3,6,7,9} and are arranged in random order.

What is the probability that the resulting 3-digit number is less than 900? 

Answer 1

The three-digit number will be less than 900 exactly if the first digit is anything but 9. So the probability that the number is less than 900 is the same as the probability that the first number is not 9, which is 4/5 = 0.8. I hope this is helpful.