2016 AMC 8 Problems/Problem 13

Two different numbers are randomly selected from the set ${ - 2, -1, 0, 3, 4, 5}$ and multiplied together. What is the probability that the product is $0$ ?

$\textbf{(A) }\dfrac{1}{6}\qquad\textbf{(B) }\dfrac{1}{5}\qquad\textbf{(C) }\dfrac{1}{4}\qquad\textbf{(D) }\dfrac{1}{3}\qquad \textbf{(E) }\dfrac{1}{2}$

Solution

The product is zero if and only if zero is one of the numbers that is chosen. 2 numbers are chosen out of 6 total, so the chance that the product is 0 is $\frac{2}{6}=\textbf{(D)} \frac{1}{3}$ .

2016 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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All AJHSME/AMC 8 Problems and Solutions

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2016 AMC 8 Problems/Problem 13

Solution