E(5) onto E(4)
Probability
Level
3
How many surjections are there from {1, 2, 3, 4, 5} onto {1, 2, 3, 4}?
The answer is 240.
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1 solution
It is equal to S(5,4) x 4! = 10 x 24 = 240
Where S(n,k) is the Stirling number of the second kind (or Stirling partition number) and is the number of ways to partition a set of n objects into k non-empty subsets