HMMT November 2020 U32

The numbers $1,2, \ldots, 10$ are written in a circle. There are four people, and each person randomly selects five consecutive integers (e.g. $1,2,3,4,5$, or $8,9,10,1,2$ ). If the probability that there exists some number that was not selected by any of the four people is $p$, compute $10000 p$.