SOLUTION: A fair six sided die is tossed. After it lands, the bottom face cannot be seen. What is the probability that the product of the visible numbers on the five faces is divisible by 12

Question 781325: A fair six sided die is tossed. After it lands, the bottom face cannot be seen. What is the probability that the product of the visible numbers on the five faces is divisible by 12?
I started by doing all of the possibilities I could think of.
For Example: 1*2*3*4*5=120 120/12=10
2*3*4*5*6=720 720/12=60
3*4*5*6*1=360 360/12=30
4*5*6*1*2=240 240/12=20
5*6*1*2*3=180 180/12=15
6*1*2*3*4=144 144/12=12
After this I didn't know what to do.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Answer is 100%.
Don't look at the 5 exposed sides, but ask which of the six sides can be down!
Any of the numbers 1 to 6 can be on the bottom and the product of the remaining five is always divisible by 12.
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