Final answer:
When three standard dice are tossed, the probability that the product of the numbers obtained equals 180 is 1/216.
Step-by-step explanation:
When three standard dice are tossed, the numbers A, B, and C represent the results. To find the probability that A*B*C = 180, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
Let's break down the factors of 180: 180 = 2^2 * 3^2 * 5. We can represent A, B, and C as the products of these factors. Consider:
A = 2 * 2 * 3 * 5 = 60
B = 2 * 2 * 3 * 5 = 60
C = 2 * 2 * 3 * 5 = 60
To calculate the probability, we need to determine the number of outcomes where A, B, and C equal 60. Each die has 6 possible outcomes (1-6), so the total number of outcomes is 6^3 = 216. There is only one combination (60, 60, 60) that satisfies the condition, so the probability is 1/216.