How many Binary trees can be made with :-
1) Un- labeled :- There is a formula called CATALAN NUMBER = $\frac{\binom{2n}{n}}{n+1}$
Called them as patterns
2) labeled :- for each pattern above, there are n! trees ===> total = $\frac{\binom{2n}{n}}{n+1} * n! $
How many Binary Search trees can be made with :-
1) Un- labeled :- There is a formula called CATALOG NUMBER = $\frac{\binom{2n}{n}}{n+1}$
Called them as patterns
2) labeled :- for each pattern above, there only 1 way to labeled the nodes of the tree ===> total = $\frac{\binom{2n}{n}}{n+1} $
How many AVL trees can be made with :-
1) with 3 un-labeled nodes:- only one way ( i don't know general formula for un-labeled )
2) labeled :- for each pattern above, there only 1 way to labeled the nodes of the tree ===> total = No.of trees with un-labeled.