how many bit strings of length 8 have at least 4 consecutive

how many bit strings of length 8 have at least 4 consecutive 0

Solution

total of number of bit strings = 2^8=256

no 0 = 1

exactly one 0 =8

exactly two consecutive 0 = C(8,2) = 7*4=28

exactly three consecutive 0 =C(8,3) = 8*7=56

number of bits strings having atleast 4 consecutive 0 = 256-(no 0+exactly one 0+exactly two consecutive 0+exactly three consecutive 0)

=256-(1+8+28+56)=163

number of bits strings having atleast 4 consecutive 0 =163...........Answer