Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 414: 37

912 strings

Total strings = $2^{10}$ = 1024 Strings with less than three $1$ = $C$(10,0) +$C$(10,1) +$C$(10,2) = 1 + 10 + 45 = 56 Strings with less than three $0$ = $C$(10,0) +$C$(10,1) +$C$(10,2) = 1 + 10 + 45 = 56 Strings with at least three $1$ and three $0$ = total strings - strings with less than three $1$ - strings with less than three $0$ = 1024 - 56 -56 = 912 strings