Combinatorics

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Moderate

Set Partitions, Stirling Numbers - S(n,n-1)

COMBIN-H9JXG4

Let $S(n,k)$ be the number of ways to partition an $n$ element set with $k$ nonempty subsets, also called "blocks."

Which of the following is equal to $S(n,n-1)$?

A

2

B

${n-1 \choose 2}$

C

${n \choose 2}$

D

$n-1$