Final answer:
The total number of different 6-length bit strings that contain the sequence 0000 is 12, derived from the sum of possibilities across the different positions where 0000 can occur.
Step-by-step explanation:
To find the number of different bit strings of length 6 that contain the string 0000, we can consider the placement of the 0000 sequence in the 6-bit string. There are three positions where the 0000 can be placed:
- At the beginning (0000XX), where XX can be any of the 22 = 4 combinations of 0 and 1.
- In the middle (X0000X), where X can be either 0 or 1, leading to 22 = 4 possible combinations.
- At the end (XX0000), which also gives us 22 = 4 combinations.
Summing the possibilities from the three positions, we have a total of 4 + 4 + 4 = 12 different bit strings of length 6 that contain the sequence 0000.