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The question is:

How many onto functions are there from a set with four elements to a set with threee elements?

If i let x = {a,b,c,d,}

y = {x,y,z}

Step 1: construct an onto function from {a,b,c} to {x,y,z}

step 2:

choose whether to send d to x or to y or to z. I directly found there are 9 ways to perorm step 1, and 3 ways to perform step 2. Thus by the multiplication rule (9)(2) = 18 ways to define functions in the first category. But the book did a simlar example and then ended up adding an additional 2 to their answer after doing the multiplication rule. So would it be 18 + 2 = 20?

The question in the book was the following:

How many onto functions are there from a set with 4 elements to a set with 2 elements?

they got an answer of 14 orginally 12 then added 2 more at the end for some reason.

THanks!