# permutation question

• Nov 24th 2013, 11:54 AM
benjamin872
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
• Nov 24th 2013, 12:12 PM
Plato
Re: permutation question
Quote:

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.

Quote:

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 $\displaystyle \|A\|\le\|B\|~.$