Is anybody here acquainted with the De Moivre-Jordan Theorem?

Cannot locate anything on the internet, so here I shall reproduce a rather terse account of it from a textbook on Fundamental Probability:

For events the probability that *exactly m *of the occur, *m *= 0*, *1*, . . . , n*, is given by

__An Example__

Given n=4, m=2, calculate the probability that exactly 2 out of 4

occur is:

where

is given by:

Looks like its something to do with the double counting like the inclusion-exclusion theory, but cannot figure it out.

Can anyone link me to the correct wiki page or try to explain to me what is happening here?