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?
1
$\begingroup$
combinatorics
elementary-set-theory
-
0Inclusion-exclusion _is_ simple combinatorics, isn't it? – 2012-08-29
1 Answers
5
You know probably the number off all functions from $\lbrace 1,2,3 \rbrace$ to $\lbrace 1,2\rbrace$ and a function which is NOT surjective must be constant since the range has only two elements.