Answer these questions based on the following informations
After completing his MBA, Zafar shifted to a new flat where he bought a new bookself and a set of 7 novels. The names of these novels, In the chronoligical order, are A,B,C,D,E, F and G
He wants to keep the novels in his bookshelf such that the last two novels of the series are never kept together, find the number of ways in which he can arrange all the novels

Options

A. 3600
B. 2500
C. 1440
D. 2880

Answer

To solve the problem of arranging the 7 novels (A, B, C, D, E, F, and G) such that the last two novels (F and G) are never kept together, we can follow these steps:

### Step 1: Calculate the total arrangements without any restrictions.
The total number of arrangements of 7 novels is given by the factorial of the number of novels. Therefore, we calculate:

\[ \text{Total arrangements} = 7! = 5040 \]

### Step 2: Calculate the arrangements where F and G are together.
To find the arrangements where F and G are together, we can treat F and G as a single unit or block. This means we now have 6 units to arrange: (FG), A, B, C, D, and E.

The number of arrangements of these 6 units is:

\[ \text{Arrangements with F and G together} = 6! = 720 \]

Since F and G can be arranged among themselves in 2 ways (FG or GF), we multiply the arrangements by 2:

\[ \text{Total arrangements with F and G together} = 6! \times 2! = 720 \times 2 = 1440 \]

### Step 3: Calculate the arrangements where F and G are not together.
To find the number of arrangements where F and G are not together, we subtract the arrangements where they are together from the total arrangements:

\[ \text{Arrangements with F and G not together} = 7! - (6! \times 2!) \]

Substituting the values we calculated:

\[ \text{Arrangements with F and G not together} = 5040 - 1440 = 3600 \]

### Final Answer:
Thus, the number of ways in which Zafar can arrange the novels such that F and G are never kept together is **3600**.

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