<s>[INST] Probability that the sum of two elements in a set is divisible by 3. Select 2 integers from the set $\{1,2,3,4,5,6,7,8\}$. What is the probability that their sum is divisible by 3? I am assuming this is without replacement although this is not explicitly stated. 
My answer: There are $\binom{8}{2}$ ways of selecting two elements. Only 6 of these pairs $(1,2), (4,5), (4,2), (7,8),(3,6), (2,7) $ are divisible by 3. Thus $P=6/\binom{8}{2}$. Is this correct?
 [/INST] Numbers can be classified as $3n$, $3n+1$, $3n+2$. Now the sum will be divisible by $3$ only if the pair is $(3n,3n)$ or $(3n+1,3n+2)$. 
Digits of type: $3n = (3,6)$; type $3n+1= (1,4,7)$; type $3n+2 = (2,5,8)$. So the number of possible would be $1 + 3\cdot 3 = 10$. $\text{Total probability} = 10/28$.
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