Number of possible permutations that can be obtained using stack for input seq

Question

Number of possible permutations that can be obtained using stack if the input sequence is 1, 2, 3, 4, 5 (in the order) is

Comments

This is Catalan Number.

https://math.stackexchange.com/questions/1431923/how-many-sequences-possible-in-stack-if-the-input1-2-3-n-is-in-order

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Im a bit confused still, can you write a solution for this?

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@h4kr There are $C_5 = 42$ possible permutations for the sequence $(1,2,3,4,5)$ using stack.

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thanks, but in the solutions of the question where is solved it from had answer: 2048 [cant say their answer is correct, i often found wrong solutions from their Q&A]

Answer 1

For stack and calculating the valid Permutation when the order of the insertion of element is defined we should use the CATALAN NO

$\frac{_{n}^{2n}\textrm{C}}{n+1}$ ie $\frac{_{5}^{10}\textrm{C}}{6}$ = 42