Final answer:
There are 16 different binary sequences of length 5 that have a 0 in the middle, calculated by considering the number of binary choices (2) for each position except for the middle one which is fixed.
Step-by-step explanation:
To determine how many binary sequences of length 5 there are that have a 0 in the middle, we must consider that the middle position of the sequence (which is the third digit) is fixed as 0. Since binary sequences can only have digits that are 0 or 1, for the remaining positions, there are two possibilities for each spot (either 0 or 1).
So for the first position, we have 2 choices (0 or 1), for the second position, we also have 2 choices, and for the fourth and fifth positions, we again have 2 choices each. Since the third position is already fixed as 0, it does not contribute additional combinations.
The total number of binary sequences of length 5 with a 0 in the middle is therefore:
2 (first position) × 2 (second position) × 1 (third position) × 2 (fourth position) × 2 (fifth position) = 16
Therefore, there are 16 different binary sequences of length 5 with a 0 in the middle.