Problem:
Bernardo randomly picks distinct numbers from the set and arranges them in descending order to form a -digit number. Silvia randomly picks distinct numbers from the set and also arranges them in descending order to form a -digit number. What is the probability that Bernardo's number is larger than Silvia's number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The probability that Bernardo picks a 9 is . In this case, his three-digit number will begin with a 9 and will be larger than Silvia's three-digit number.
If Bernardo does not pick a 9, then Bernardo and Silvia will form the same number with probability
If they do not form the same number then Bernardo's number will be larger of the time.
Hence the probability is
The problems on this page are the property of the MAA's American Mathematics Competitions