Four standard six-sided dice are rolled. What is the probability that the product of the numbers on the top faces of all four dice is \(24\)? Express your answer as a common fraction.
+23252 The way that you can get a product of 14 is: 1 x 1 x 4 x 6 12 ways
or 1 x 2 x 2 x 6 12 ways
or 1 x 2 x 3 x 4 24 ways
or 2 x 2 x 2 x 3 4 ways
The number of possible ways is 1296.
Can you find the probability from these parts?
1138 , 1146 , 1164 , 1183 , 1226 , 1234 , 1243 , 1262 , 1318 , 1324 , 1342 , 1381 , 1416 , 1423 , 1432 , 1461 , 1614 , 1622 , 1641 , 1813 , 1831 , 2126 , 2134 , 2143 , 2162 , 2216 , 2223 , 2232 , 2261 , 2314 , 2322 , 2341 , 2413 , 2431 , 2612 , 2621 , 3118 , 3124 , 3142 , 3181 , 3214 , 3222 , 3241 , 3412 , 3421 , 3811 , 4116 , 4123 , 4132 , 4161 , 4213 , 4231 , 4312 , 4321 , 4611 , 6114 , 6122 , 6141 , 6212 , 6221 , 6411 , 8113 , 8131 , 8311 , Total = 64 such numbers
The probability is: 64 / 6^4 ==4 / 81
+2511 Yes, Mr. !!!BB, you and your fucking computer can solve this just fine ...and step on Geno’s partial solution, which he presented as he did, leaving some of the solution process for the dumbshit that asked the question.
You are obsessed. When you see an asshole you just gota stick your dick in it. You can’t help yourself.... 
GA
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+2511 Is this a rhetorical question? Even if it is, it still needs a question mark (?). I’ll answer your question about why I’m rude and crude, if you restate it using a question mark, and tell me why you are so dumb –that way I’ll know how much to dumb-down my explanation.
As for Mr. BB’s helpful answers, they are often wrong, and this one certainly is wrong! (There are no eights (8) on a standard die. Even when !!!Mr. BB’s answers are correct, they do not demonstrate math solutions. At best they confirm an answer. (In case you are wondering, my comment, “Yes, Mr. !!!BB, you and your fucking computer can solve this just fine,” is sarcasm.)
If Mr. !!!BB’s post was the only one on this thread, I may or may not have commented. If so, it would be about its accuracy. I cherry-pick when and if I comment on !!!Mr. BB’s screwups, else I wouldn’t have much time for anything else.
But here, Mr. !!!BB stepped on Geno’s teaching post. Why? Rudeness? Arrogance? Obsessive-compulsive behavior? Maybe all of them...
I estimate Geno has about 45 years of teaching experience for high school and collegiate mathematics. He knows mathematics and he knows how to teach it to the brilliant and the dumb –even on a forum that’s setup primarily for tutoring and not conducive for teaching.
I think a little respect for Geno is a minimum ideal.
GA
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