Question:

Step 1: The number of ways to select 4 novels from 6 different novels is given by the combination formula: $$C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4!2!} = \frac{6 \times 5}{2 \times 1} = 15$$ Step 2: The number of ways to select 1 dictionary from 3 different dictionaries is given by the combination formula: $$C(3,1) = \frac{3!}{1!(3-1)!} = \frac{3!}{1!2!} = 3$$ Step 3: A total of 5 items (4 novels and 1 dictionary) are selected. These 5 items are to be arranged in a row on a shelf such that the dictionary is always in the middle. This means the dictionary occupies the 3rd position in a row of 5 positions. Step 4: The 4 selected novels must be arranged in the remaining 4 positions (positions 1, 2, 4, and 5). The number of ways to arrange these 4 distinct novels is given by the permutation formula: $$4! = 4 \times 3 \times 2 \times 1 = 24$$ Step 5: The selected dictionary is placed in the middle position. Since there is only 1 dictionary selected, and it must be in the middle, there is only 1 way to place it once it's selected. The total number of such arrangements is the product of the number of ways to select the novels, the number of ways to select the dictionary, and the number of ways to arrange the novels: $$ \text{Total arrangements} = C(6,4) \times C(3,1) \times 4! $$ $$ \text{Total arrangements} = 15 \times 3 \times 24 $$ $$ \text{Total arrangements} = 45 \times 24 $$ $$ \text{Total arrangements} = 1080 $$