Answer
a) 120
b) 386
c) 176
d) 968
Work Step by Step
a) Exactly three $0s$ = $C$(10,3) = 120
b) More $0s$ than $1s$ i.e. number of $0s$ can be 6,7,8,9,10
Number of strings = $C$(10,6)+$C$(10,7)+$C$(10,8)+$C$(10,9)+$C$(10,10) = 210 + 120 + 45 + 10 + 1 = 386
c) At least seven $1s$ = $C$(10,7)+$C$(10,8)+$C$(10,9)+$C$(10,10) = 120 + 45 + 10 + 1 = 176
d)At least three $1s$ = Total strings - String with less than three $1s$ = $2^{10}$ - ($C$(10,0) + $C$(10,1) + $C$(10,2)) = 1024 - (1 + 10 + 45) = 968
