Question

The number of surjections
that can be defined from
{1,2,3,4,5,6
is​

Answer 1

Answer:

Where A={1,2,3,4,5,6} and B={a,b,c,d,e}.

My book says it's:

Select a two-element subset of A.

Assign images without repetition to the two-element subset and the four remaining individual elements of A.

This shows that the total number of surjections from A to B is C(6,2)5!=1800.

I'm confused at why it's multiplied by 5! and not by 4!. Also in part 2, when we assign images, do they mean images in B?