2016 AMC 8 Problems/Problem 13
Contents
Problem
Two different numbers are randomly selected from the set and multiplied together. What is the probability that the product is
?
Solutions
Solution 1
The product can only be if one of the numbers is 0. Once we chose
, there are
ways we can chose the second number, or
. There are
ways we can chose
numbers randomly, and that is
. So,
so the answer is
.
Solution 2
There are a total of possibilities, because the two numbers that being multiplied are being picked at the same time, so there are
possibilities that zero is being chosen because another number is already being chosen. We want
to be the product so one of the numbers is
. There are
possibilities where
is chosen for the first number and there are
ways for
to be chosen as the second number. We seek
.
Solution 3 (Complementary Counting)
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
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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