Question

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.

Answer 1

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.