I know the principle of inclusion-exclusion and solved some problems related to this principle but I don't know how this principle was discovered? Whenever I use this principle I was amazed thinking of how the concept of the principle of inclusion-exclusion came into the mathematicians head? Can anyone tell me how mathematician discovered the principle of inclusion-exclusion in combinatorics? What problems led them to introduce the the principle of inclusion-exclusion?
You can see Inclusion–exclusion principle :
The name comes from the idea that the principle is based on over-generous inclusion, followed by compensating exclusion. This concept is attributed to Abraham de Moivre (1718); but it first appears in a paper of Daniel da Silva ("Proprietades geraes et resolucao das Congruencias biniomis", Lisbon 1854), and later in a paper by J.J. Sylvester (1883).
The source seems reliable; see :
- Leonard Eugene Dickson, History of the Theory of Numbers, Volume I: Divisibility and Primality (1919), page 119.