Answer
a) 220
b) 299
c) 4017
d) 924
Work Step by Step
a) Exactly three $1s$ = $C$(12,3) = 220
b) At most three $1s$ = $C$(12,3) + $C$(12,2) + $C$(12,1) + $C$(12,0) = 220 + 66 + 12 + 1 = 299
c) At least three $1s$ = all possible strings - at most three $1s$ + exactly three $1s$= $2^{12}$ - 299 + 220 = 4017
d) Equal $0s$ and $1s$ i.e. six $1s$ =$C$(12,6) = 924
