Final answer:
To find the number of bit strings with exactly five 0s and fourteen 1s where each 0 is followed by two 1s, treat each '011' sequence as a single entity. Then, arrange these entities along with the remaining 1s, accounting for indistinct items, which results in the formula 14! / (5! * 9!).
Step-by-step explanation:
The number of bit strings that contain exactly five 0s and 14 1s, where every 0 must be immediately followed by two 1s, can be determined using combinatorial methods. Since each zero must be followed by two 1s, the sequence 011 is treated as a single entity. Hence, we effectively have five '011' sequences and an additional nine 1s to arrange.
The total number of entities to arrange is five '011' sequences plus nine 1s, which gives us 14 entities in total. This can be thought of as arranging 14 distinct items, which can be done in 14! (14 factorial) ways. However, since the '011' sequences and the 1s are not distinct amongst themselves, we should divide by the number of ways each set of indistinct entities can be arranged. Therefore, we divide by 5! (to account for the identical '011' sequences) and by 9! (to account for the identical 1s).
The formula becomes 14! / (5! * 9!), which is the number of bit strings with exactly five 0s each followed by two 1s, along with 14 1s in total.