Given the set:
has n elements.
If 
, how many total mappings are there from the set 
to the set ? How many bijective mappings are there between them?
For what value of n does the set 
have 128 subsets?
For what value of n, does the set has five times as many three-element subsets as two-element subsets?
Prove by mathematical induction that the sum of all elements of the set is equal to 
.
