I know we can use inclusion-exclusion principle or stirling numbers to solve this for a set of n elements onto a set of m elements. But I wanted to know how can we get the result using simple combinatorics as the number of elements here is too less.
How many surjections are there from a set of 3 elements onto a set of 2 elements?
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combinatorics
elementary-set-theory
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2Do you mean the numbers $3$ and $2$ are too small to evaluate [$2!\,\genfrac\{\}0{}32$](http://en.wikipedia.org/wiki/Twelvefold_way#Surjective_functions_from_N_to_X)? Curious. – 2012-08-29
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0Inclusion-exclusion _is_ simple combinatorics, isn't it? – 2012-08-29