Inserting the keys into hash table
Open addressing is the hashing technique in which for inserting an element in the table firstly we search for the elements if it is already contained in it, the search returns either the element or the free space in the array to fill that element.
In uniform hashing technique sequence of elements to be search
can be any of the m! permutation in
that is this
technique gives the method of searching which search in the full
list for the single element in the generalized way.
When the first key inserted, it has m choices out of
m, the second key has 
choices out
of m so on, key n has 
choices out
of m. The insertion of these keys is independent of each
other,
Thus probability:
……(1)
Hence from equation (1) the probability is as:
By theorem for the n keys to be inserted in a table where
then the probability of occurring a match in the table is less
than
, it is very
efficient to find the hash function for which there is no
collisions in a static set K containing n keys.
When the number of key values n exceeds
, that is a
hash table of size 
that is
is
excessive. Hence in this case we use the hashing technique at the
two levels, in the first level or at the outer level the hash
function 
to hash the
keys into 
slots.
Then, if 
the
keys
hash to slot j. we use a secondary hash table 
of size
it
gives a set having invariant or constant time without any
collisions in the table.
Hence, in a hash table of capacity m for inserting
n keys by open addressing and uniform hashing techniques
then the probability of collisions to occur is 
where
.