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The probability that the product of the three integers can be divisible by 10 is obtained by randomly taking three times from nine integers from one to nine, one at a time I read the answers on the Internet, but I can't understand them, especially the ones with one five and two five. I don't know how to calculate the probability I thought there must be a 5 that is 1 / 9, there must be an even number 4 / 9, another random 9 / 9, but the multiplication is not right 214, why not? It's best to write the reason step Otherwise I can't understand it
Among the nine numbers from 1 to 9, there are three times to take them back, and all of them are 9 * 9 * 9 = 729
The product of the three numbers can be divided by 10
There are two 5's and one even number (type 552) in the formula 1 * 1 * 4 * C (3,1) = 4 * 3 = 12 (species)
The method of one 5 and two even numbers (type 522) is 3 * 4 * 4 = 48
Or 1 * 4 * C (3,1) + 1 * C (4,2) * P (3,3) = 4 * 3 + 6 * 6 = 48 species
There are 1 * 4 * 4 * P (3,3) = 16 * 6 = 96 (species)
The probability is (12 + 48 + 96) / 729 = 156 / 729 = 52 / 243 ≈ 0.21399177 ≈ 0.214
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