Calculating Possible Combinations of Bases in a DNA Strand of a Given Length
At each base, you can have 4 different bases (A,T,C or G). Therefore for the first base there are 4 possibilities, namely


A
T
C
G


For the first two base pairs there are $4^2 = 16$ possible combinations


AA
AT
AC
AG
TA
TT
TC
TG
CA
CT
CC
CG
GA
GT
GC
GG


For the first three bases, there are $4^3$ possible combinations. For 8 base pairs, there are $4^8 = 65536$ possible combinations. $2^8$, $8!$ and $8! + 2^4$ are all wrong.