Track / Stage 4 / 40 of 340 #300 of 2000

Problem 300

AMC 12 late, AIME early

Combinatorics Difficulty 4.6 Find the answer

13. Two different numbers are randomly selected from the set $\{-2,-1,0,3,4,5\}$ and multiplied. The probability that the product is 0 is ( ).
(A) $\frac{1}{6}$
(B) $\frac{1}{5}$
(C) $\frac{1}{4}$
(D) $\frac{1}{3}$
(E) $\frac{1}{2}$

Your answer

Official solution

13. D.
$P=\frac{\mathrm{C}_{5}^{1}}{\mathrm{C}_{6}^{2}}=\frac{5}{\frac{6 \times 5}{2}}=\frac{1}{3}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.