SOLVED:The number of partitions of a set of n elements into k distinguishable boxes (some of which may be empty) is k^n. By counting in a different way, prove that k^n=( k 1) 1 ! S(n, 1) ( k 2) 2 ! S(n, 2) ⋯ ( k n) n ! S(n, n) (If k>n, define S(n, k) to be 0 .)
SOLVED:The number of partitions of a set of n elements into k distingui…
Jun 8, 2021
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