Since the string can begin with 00 and also end with 111, this is an example of an inclusive problem. So you'll need to add the two amounts together but then subtract their intersection.

2^5 + 2^4 - 2^2

(the 2^2 are the number of strings that look like this: 00**111)

Infinitely many if the numbers are not restricted to being integers.

2)

x1 x2 x3 are not negative numbers.

we have: x1 + x2 + x3 = 11

How many solutions would there be for the equation?

ok so im thinking each x can have numbers 0 -11.

so 11 * 11 * 11 different solutions.