Three distinct numbers are selected at random from the set {1,2,3,4,5,6}. what is the probability that their product is divisible by 3?

The total number of combinations of 3 from 6 = 6C3 =  20
All possible combinations of 3  which have a product divisible by 3 must contain either a 3 or a 6. 
So the number not divisible must be  3 combinations from the number 1, 2, 4 and 5.= which is 4

So the required probability is 20-4 ? 20  = 16/20 =  0.8 Answer

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