There are not 56 cases where two numbers are adjacent. There are duplicates. For example, if you choose 23, then choose 4; Then, choose 34, then choose 2, and so on.

P(ξ=2)=7/84= 1/ 12

p(ξ= 1)=(2×6+6×5)/84 = 1/2

Choose two adjacent ones first, and then choose one that is not adjacent. There are two kinds of two adjacent ones: if it is 12 or 89, you can choose six; If it is other, there are five kinds.

P(ξ=0)=5/ 12

The mathematical expectation is 2/3.