The Farm Agency is to use only the letters A, B, and C to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

this question has been asked 2 other times already too
http://openstudy.com/study#/updates/5115b363e4b09e16c5c82f80
http://openstudy.com/study#/updates/53590f1fe4b017db97e40a51

Question

The Farm Agency is to use only the letters A, B, and C to make tags. Let y be the number of tags they can make using n spaces. What is the formula for the number of tags they can make?

this question has been asked 2 other times already too 
http://openstudy.com/study#/updates/5115b363e4b09e16c5c82f80
http://openstudy.com/study#/updates/53590f1fe4b017db97e40a51

anonymous · Answer

Ok so lets attempt to explain this for a tag with 2 alphabets
__ , ___ 
So for the first "space" you have 3 options: a,b or c
For the second space you have 3 options: a,b or c
so we have 3*3=9
There are 9 possible options of tags using the 3 alphabets:
AA
AB
AC
BA
BB
BC
CA
CB
CC

anonymous · Answer

im only a fan @theopenstudyowl

anonymous · Answer

So for 3 spaces we would have
3*3*3=3^3
For 4 spaces we would have 
3*3*3*3=3^4
In general since you are allowed repetition and order matters 
we have the following equation
3^n=y