"Find the number of surjective functions $f: A->B$, where$ A = \{1,2,3,4,5,6\}, B = \{1,2,3,4\}$ and where $f(1) > f(2) > f(3)$."
I know how to find # of surj. functions from $ A->B $ (in this case $4^6 $minus all maps to subsets of B). But I don't know how to implement this condition$ f(1) > f(2) > f(3)$.
I think it is important to calculate maps of $\{1, 2, 3\}$, I have found 4 ways how to do the mapping, simply by writing all the possible ways (I think it is 4 choose 3 since there is only one way how to order). Then I need to assign some $(>=1)$ elements from $\{4, 5, 6\}$ to the remaining element of $B$ (for the function to be surjective) and keep in mind that $\{4, 5, 6\}$ can also be assigned to other els of$ B$.
Can you please give me an advice how to do it? Thank you