Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. How to embed $S_{n-1}$ into $S_n$ in $n$ ways?
2026-03-30 13:26:11.1774877171
How to embed $S_{n-1}$ into $S_n$ in $n$ ways?
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Hint: in how many ways can you pick $n-1$ different elements from the set $\{1,2, \cdots , n-1, n\}$?