$($a$)$ Insert the following keys: $911,925,862,920,813$ and $791,$ into a hash table with hash function H$($key$)=$ key mod $7,$ using linear rehashing as collision resolution strategy. Show the hash table after all the insertions and show the computations of the hash function. $[5]($b$)$ How many probes are required to store $920$ and $813?[1]($c$)$ How many probes are required to conclude that key $841$ is not in the table? $[1]($d$)$ Remove the key $855$ from the hash table and show the hash table. $[1]($e$)$ What is the average number of probes needed to find a value that is not in the table? $[2]$