Splitting notes between students and counting functions between sets

[sintec]

I need a little help with combinatorics.

2 Students have 6 dollar notes worth 500 dollars, and 4 notes worth 1000 dollars. Notes with the same value are not distinguished.
A-How many ways to split the notes
B-How many ways to split the notes, so that both get an equal amount of notes.
C-How many ways to split the notes, so that both get an equal amount of money.
D- How many ways to split the notes if we distinguish the notes among each other.

And another:

There is given a set M with m elements and set N with n elements and function f:M->N
A- How many diferent bijective functions exist when m=n?
B- How many diferent injective functions exist when m<=n?
C- how many diferent surjective functions exist when m>=n?

thx!

 

[matt grime]

FOr the second one, as always, the answer is 'count'. Label the elements of M arbitrarily, the first can be sent to how many options? now take the second element, what do the restrictions on the type of function mean? so how many of the elements of N can it map to? rinse, repeat. that'll do a nd b, c needs you to think some more, but dont' give up. mathematics questions , if they jhave any merit, aren't supposed to be solved immediately.