How many binary strings $(\text{'}$binary$\text{'}$ means each number of the string can either be $00$ or $11)$ of length$-$nn can be formed such that no two consecutive numbers are identical? $($ie$,010010$ is a binary string of length$-33$ that satisfies this statement$).$ Assume n$1$n$1.$

For the following options, assume k$=2$k$=2$ since there are two choices for each position$--11$ or $00.$

The following multiple$-$choice options contain math elements, so you may need to read them in your screen reader's $$reading$$ or $$browse$$ mode instead of $$forms$$ or $$focus$$ mode.

Choice $1$ of $8$: $2$k$2$kChoice $2$ of $8$: None of theseChoice $3$ of $8$: n$!$k$!($n$$k$)!$k$!($n$$k$)!$n$!$Choice $4$ of $8$: $2$n$2$nChoice $5$ of $8$: $22$Choice $6$ of $8$: nknkChoice $7$ of $8$: knknChoice $8$ of $8$: n$!($n$$k$)!($n$$k$)!$n$!$