1. ## permutation question

I am trying to clear something up in my head, if I have the below

set1 of {A,B,C,D,E,F,G}
set2 of {w,x,y,z}

My question how many ways can set1 map to set2, well 6X4=24 ways

but what if I had 10 or 10million sets of 'x,x1,x2,xbla' number of elements then what formula would I have to use for an ordered mapping set1 ->set 2>set3

just multiply the number of elements in each set together?

Could someone explain briefly the approach for this on permutations and combinations, with and without repetition.

Many thanks

2. ## Re: permutation question

Originally Posted by benjamin872
I am trying to clear something up in my head, if I have the below
set1 of {A,B,C,D,E,F,G}
set2 of {w,x,y,z}

My question how many ways can set1 map to set2, well 6X4=24 ways this is incorrect
The correct answer is $\displaystyle 4^7$. Let $\displaystyle \|A\|$ stand for the number of in the finite set $\displaystyle A$.

The number of functions from $\displaystyle A\to B$ is $\displaystyle \|B\|^{\|A\|}$ That is the total number.

Originally Posted by benjamin872
Could someone explain briefly the approach for this on permutations and combinations, with and without repetition.
The only way to do it without repetition is if $\displaystyle \|A\|\le\|B\|~.$