How many different (full/complete) in-order binary-trees do exist?
Q1: How many different binary-trees do exist?
A1: c(n) = (2n)! / ((n + 1)! * n!) → c(4) = 14  

Q2: How many different complete binary-trees do exist?
A2: Exact one:  

;       (3)        L0: full
;      / | \
;   (2)  |  (4)    L1: full
;   /|   |   |
; (1)|   |   |     L2: not full (Node 2 is missing right child)
;  | |   |   |
;  1 2   3   4     Complete?: Yes, because all (but last) levels are full.


Q3: How many different full binary-trees do exist?
A3: If n is odd: c((n-1)/2) else 0. n = 4 therefore 0. Reference

Thanks to YuvalFilmus for the help!