For a random graph, G, on n vertices's, each possible edge is present independently with probability k, 0 <= k <= 1.

I seek P(all edges between these vertices's are present in G)
My thoughts so far

If we have the empty subset, p = 1
If we have a one element set, p = 1
If we have a two element set, p = k
If we have a three element set, p = k^3
If we have a four element st, p = k^6
If we have a five element set, p = k^10.

If the above is correct, then I can capture the probability as the following:  P = k^(n C 2)