Q53

A hash table of length $10$ uses open addressing with hash function $h(k) = k \: \mod \: 10$, and linear probing. After inserting $6$ values into an empty hash table, the table is shown as below

$$\begin{array}{|l|l|}\hline \text{0} & \text{} \\ \hline \text{1} & \text{} \\\hline \text{2} & \text{42} \\ \hline \text{3} & \text{23} \\\hline \text{4} & \text{34} \\\hline \text{5} & \text{52} \\\hline \text{6} & \text{46} \\\hline \text{7} & \text{33} \\\hline \text{8} & \text{} \\\hline \text{9} & \text{} \\\hline \end{array}$$

How many different insertion sequences of the key values using the same hash function and linear probing will result in the hash table shown above?