Final answer:
To find the number of bit strings of length n that start and end with 1s, we only consider the n-2 positions between the first and last bits. Since each of these can be either 0 or 1, the total number of such bit strings is 2^(n-2).
Step-by-step explanation:
The question you are asking is related to the concept of counting bit strings in the field of combinatorics, a branch of mathematics that deals with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Since you want to know how many bit strings of length n, where n is a positive integer, start and end with 1s, we'll answer this comprehensively.
Let us denote the length of the bit string as n. Since the first and the last bit must be 1, we are only concerned with the n-2 positions in between the first and the last bits. These n-2 positions can be either 0 or 1, giving us two choices for each position. Therefore, the total number of different bit strings that start and end with 1 is 2n-2.
To elucidate this further, let's visualize a bit string of length 5 that starts and ends with 1:
1 _ _ _ 1
For the three positions denoted by the underscores, we have 2 choices (either 0 or 1). So, the number of different bit strings that satisfy the conditions is 23 = 8.