Max has eight identical cups. Each cup contains a different combination of nickels, dimes and quarters, each totaling 45 cents. Max randomly selects a cup. What is the probability that the cup he selects contains at least three dimes? Express your answer as a common fraction.

The possible combinations for 5c nickels, 10c dimes, and 25c quarters to make up 45c are:

25+10*2

25+10+5*2

25+5*4

10*4+5

10*3+5*3

10*2+5*5

10+5*7

5*9

These are all 8 possibilities, and there are no others.

The only possibilities with 3 or more dimes are:

10*4+5

10*3+5*3

Since only 2 of the 8 possibilities satisfy the requirement, then the probability of selecting a cup with at least 3 dimes is 2/8, or 1/4.