Given a hash table of size $15,$ integer keys $k,$ and a hash function $h$

$h_1(k)=k\%15$

In which slots are $17$ and $18$ entered?

$17$:

$18$

Assume $17$ and $18$ have been entered using $h_1$

If we use linear probing $($step $=1),$ in which slot is $32$ entered next?

How many collisions occurred?

Instead, if we use quadratic probing, in which slot would $32$ be entered next?

How many collisions would occur?

Suppose we start from an empty HashTable but this time we use double hashing.

$h_1(k)=k\%15$

$h_2(k)=7-k\%7$

Assuming that $17$ and $18$ have been entered into the new HashTable, where is $47$ entered next?

How many collisions occurred?