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 $\displaystyle B_1, .......B_n,$ the probability that *exactly m *of the $\displaystyle B_i$ occur, *m *= 0*, *1*, . . . , n*, is given by

$\displaystyle \sum_{i=m}^n (-1)^{i-m} {i\choose m} S_i$

__An Example__

Given n=4, m=2, calculate the probability that exactly 2 out of 4 $\displaystyle B_i$ occur is:

$\displaystyle P_{2,4}= {2\choose 2} S_2 - {3\choose 2} S_3 + {4\choose 2} S_4$

$\displaystyle

= \sum_{i<j} P(B_i B_j) - 3\sum_{i<j<k} P(B_i B_j B_k) + 6 P(B_1 B_2 B_3 B_4)$

where

$\displaystyle \sum_{i<j} P(B_i B_j)$ is given by:

$\displaystyle P(B_1 B_2) + P(B_1 B_3) + P(B_1 B_4) + P(B_2 B_3) + P(B_2 B_4) + P(B_3 B_4)$

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?