  In this paper the decay of $B^+_c$ meson, consisting of two b and c heavy
quarks, into the $D^0$ and $K^+$ mesons is studied. Given that the experimental
branching ratio for this decay is within the range of $3.72\times 10^{-5}$ to
$11.16\times10^{-5}$ and in our estimating the theoretical result by using the
QCD factorization approaches is $10^2$ times less than experimental one (we
have obtained $1.41\times10^{-7}$), it is decided to calculate the theoretical
branching ratio by applying the final state interaction (FSI) through the T and
cross section channels. In this process, before the $B^+_c$ meson decays into
two final state mesons of $D^0K^+$, it first decays into two intermediate
mesons like $J/\psi D^{*+}_s$, then these two mesons transformed into two final
mesons by exchanging another meson like $D^0$. The FSI effects are very
sensitive to the changes in the phenomenological parameter that appear in the
form factor relation, as in most calculation changing two units in this
parameter, makes the final result multiply in the branching ratio, therefor the
decision to use FSI is not unexpected. In this study there are nineteen
intermediate states in which the contribution of each one is calculated and
summed in the final amplitude. Therefore, the numerical value of the branching
ratio of $B^+_c\rightarrow D^0K^+$ decay is obtained by calculating the FSI
effects from $1.17\times10^{-5}$ to $11.65\times10^{-5}$ which is consistent
with the experimental result.
