$1.$ There are $6$ objects A $=\{$a$1,$ a$2,$ a$3,$ a$4,$ a$5,$ a$6\}$ and $6$ agents N $=\{1,2,3,4,5,6\}.$ No one owns an object initially. Agents have the following preferences over A $($if object aj comes before object ai in the list it is strictly preferred$)$: Agent $1$: a$3$a$2$a$1$a$4$a$5$a$6$ Agent $2$: a$3$a$2$a$1$a$4$a$5$a$6$ Agent $3$: a$2$a$6$a$5$a$4$a$1$a$3$ Agent $4$: a$4$a$2$a$5$a$6$a$3$a$1$ Agent $5$: a$1$a$2$a$3$a$6$a$4$a$5$ Agent $6$: a$2$a$6$a$3$a$1$a$4$a$5($a$)$ use RSD to find a core allocation when $(1,3,4,2,6,5)$ is the realization of the random ordering. $($b$)$ do the same when $(5,4,2,6,3,1)$ is the realization of the random ordering?