Hi, I am Emon and I am back this time to provide you with some ideas regarding the ''Inclusion and Exclusion Principle" , which is a really important topic that we should learn for olympiads. The I nclusion-Exclusion Principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets, which is given by the formula $$\left|A\cup B\right| = \left|A\right|+\left|B\right| - \left|A\cap B\right|.$$ where $A$ and $B$ are two finite sets and $|X|:=$ cardinality of set $X$, $i.e.$ the number of elements present in the set $X$. The proof of this formula can be understood directly from the above venn diagram. Additional Note (though a bit out of context). Let $\mathcal{S}$ be a discrete sample space. Then, if $A, B\subset \mathcal{S}$ are two events, then we may write $$\mathbb{P}(A\cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B),$$ which is equivalen...