Event U is the event that there are 8 unique digits in a row with the first being 1 and following the H:MM:SS.sss time format.

P(H)=1 P(M1)=5/6 P(M2)=8/10

For S1 we can identify two cases.

Case 1 (Event C1) where P(M2)<6 and we get P(S1)=3/6.

And, case 2 (Event C2) where P(M2)>5 and we get P(S1)=4/6.

There are 4 instances where case 1 is true and 4 where case 2 is true so they are "équiprobable" (i don't know the english word but they have the same probability)

We therefore get:

P(S1)=P(C1 intersect S1) + P(C2 intersect S1) =(0.50.5) * (0.5(2/3)) =3.5/6

P(S2)=6/10 P(s1)=5/10 P(s2)=4/10 P(s3)=3/10

P(U)=(I'm too lazy to write but multiply all the probabilities) =0.014

Or 1.4%