Answer
240 bit strings
Work Step by Step
The number of strings beginning with 101 is $2^{7}$ since every bit after 101 can be either 0 or 1.
By similar logic, we get the number of strings that end with 010 i.e $2^{7}$.
The number of strings that start with 101 and end with 010 is $2^{4}$ as there are only 4 bits that have to be filled.
So the solution is $2^{7}$.+$2^{7}$.-$2^{4}$ = 240.
