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國立中央大學 2026 · 考試 · 第 8 題

If a series of distinct numbers of length $n$ are pushed onto a stack in sequence, and can be popped at any time during the process (as long as the stack is not empty), how many different valid permutations can be generated?

(A)
$\dfrac{1}{n}\dbinom{2n}{n+1}$
(B)
$2^n$
(C)
$\dfrac{1}{n+1}\dbinom{2n}{n}$
(D)
$(n+1)!$

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