Final answer:
To find the number of arrangements where 4 novels and 1 dictionary are selected and the dictionary is always in the middle, we can use the combination formula. The total number of arrangements is 15.
Step-by-step explanation:
To find the number of arrangements where 4 novels and 1 dictionary are selected and the dictionary is always in the middle, we first need to choose the positions for the novels. There are 6 novels to choose from, but we need to choose 4. This can be done in C(6,4) = 15 ways.
Next, we need to choose the position for the dictionary. Since it always goes in the middle, there is only 1 option.
Therefore, the total number of arrangements is 15 * 1 = 15.
The question asks us to calculate the number of arrangements of 4 novels and 1 dictionary on a shelf with the dictionary always being in the middle. First, we choose 4 novels out of 6, and 1 dictionary out of 3. The number of ways to choose the novels is C(6,4), which equals 15, and the number of ways to choose the dictionary is C(3,1), which equals 3. After choosing the books, the novels can be arranged in 4! ways, since the dictionary's position is fixed. Therefore, the total number of arrangements is 15 x 3 x 4! (15 x 3 x 24), which equals 1080. As such, the number of such arrangements is at least 1000.