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sets

Let A:= (a1,a2,a3) and B:= (a1,a2,a3,a4,a5)
how many f : A ->B are there? (is this one 5 choose 3 + 5 choose 2 + 5 choose 1, i.e 25)
how many injective f : A ->B are there? would tho just be 5 choose 3? i.e 10?
iconic_panda
..

Your answers are *much* too small.

For a general f: A->B.

How many choices are there for f(a1)? For f(a2)? For f(a3)? So the total number of options is...?

If you require f to be injective, once you've chosen f(a1), how many choices does this leave for f(a2)? And then after that, how many choices are there for f(a3)...?
ohhh so part a is 5^3 and the other part is 5*4*3
Original post by DFranklin
Your answers are *much* too small.

For a general f: A->B.

How many choices are there for f(a1)? For f(a2)? For f(a3)? So the total number of options is...?

If you require f to be injective, once you've chosen f(a1), how many choices does this leave for f(a2)? And then after that, how many choices are there for f(a3)...?
Original post by Iconic_panda
ohhh so part a is 5^3 and the other part is 5*4*3

Yes.
thanks!
Original post by DFranklin
Yes.

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