2016 AMC 8

Solution 1

. Identify the total number of ways to select two different numbers from the set:

The set has elements. The number of ways to choose different numbers from is given by the combination formula: .

. Identify the favorable outcomes:

For the product to be zero, one of the chosen numbers must be zero. The set contains one zero (). To have a product of zero, we need to choose and any other number from the remaining five numbers .

The number of ways to choose 0 and one other number from the remaining five is .

. Calculate the probability:

The probability is the number of favorable outcomes divided by the total number of outcomes: .

Thus, the probability that the product is is

Solution 2 

Because the only way the product of the two numbers is is if one of the numbers we choose is we calculate the probability of NOT choosing a We get Therefore our answer is