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Discrete Math : 'Onto' Functions

To figure how many 'one-to-one' functions' there are from a set with 3 elements to a set with 4 elements --would be-- 4!/(4-3)! or 24.

How do you figure out how many 'onto' functions there are from a set with 4 elements to a set with 3 elements?

Please give solution and detailed explanation.

Thank you.

Solution Preview

Suppose I have two sets X={a,b,c} and Y={1,2,3,4}. I can define a function f from X to Y.
If f is one-to-one, since |X|=3, then |f(X)|=3. We know f(X) is a subset of Y, and |Y|=4, then we need to find 3 elements out of 4 in Y to make the image of f. There are C(4,3)=4! / 3!(4-3)!. Now after I select 3 ...

Solution Summary

'Onto' Functions are investigated.

$2.19