Binary strings with four non-consecutive $1$s

Question

We have a binary sequence of 1s and 0s, and the length is 10. I wonder how many binary sequence of length 10 with four 1's can be created such that the 1's do not appear consecutively?

Answer 1

Hint: There are $\binom{10}{4}=210$ ways for choosing $4$ objects among $10$ objects.
The number of the following strings $$ 1111000000,\; 0111100000,\;\ldots,\; 0000001111 $$ is $7$, hence the answer is given by $210-7=\color{red}{203}$.

Answer 2

From the wording of the question, I take it to mean that no two $1's$ occur consecutively.

Then the $1's$ must have been at any $4$ of the $7$ bullets in $\binom74 = 35$ ways

$\bullet 0 \bullet 0 \bullet 0 \bullet 0 \bullet 0 \bullet 0 \bullet $