you can think this way
you have a string of length 10 and you have two letters to use : eight "01"s and two "1"s.
ie. You have ten spaces, eight filled by "01" and two filled by "1"
In other words, there are 10 locations in the string and you're choosing 2 of them to be special,
so the answer is = ^{10}C_{2 }= 45