permutation

Question

consider a stack A with 4 elements a,b,c,d with a being top of the stack . satck B is empty . an element popped out of stack A printed imidiatly or pushed to stack B. an entry popped out of stck B can only be printed . in tis arrangement how many numbers of possible permutation will be there to print output?

Comments

12 ?

Answer 1

The answer for generalized N items is the Nth catalan number .

Given by $F(N) = \sum_{0}^{N-1} F(N-1-i)*F(i) = C_{n}^{2n}/(n+1)$

So the answer for N=4 is 14

Answer 2

i think 4! = 24 will be answer