Isn't probability a branch of combinatorics? I've heard it a lot that Probability is a branch of Statistics(which isn't a branch of mathematics) but as far as I know(High School) it appeals more as the branch of Combinatorics though.
So, can you kindly explain the reasoning behind considering Probability as a branch of Statistics and not as Combinatorics(& Maths in general).
 A: Although you're apparently familiar with the calculation of probabilities in situations where there are only a finite number of possible outcomes, probability theory also works for situations where there are infinitely many (in fact uncountably infinitely many) outcomes. Combinatorics isn't applicable to such situations.  
A: Obviously, categorization of different fields of mathematics is subjective.
But personally, I would not say that probability is a branch of combinatorics.  Rather, I would say that combinatorics and probability are distinct fields that have many applications to each other.
Combinatorics has many applications to probability, since any finite counting problem can be interpreted probalistically.  If I say that a set $S$ has $n$ elements (a combinatorial statement) then I can deduce that the probability of choosing a particular $x \in S$ with the uniform distribution over $S$ is $1/n$.  This is trivially true, but this shows that knowing the sizes of finite sets is important in probability.
Probability also has many applications to combinatorics.  In particular, the field of probabilistic combinatorics uses probabilistic methods to prove combinatorial statements.
However, there are many facts in probability that cannot be reduced to what I would think of as combinatorics.  In particular, the field often makes use of continuous distributions over infinite sets (such as the Gaussian distribution).  Here probability has much more in common with the field of real analysis, which concerns various generalizations and applications of the methods of calculus and real-valued functions.  
