In how many types ways can five different examination papers of maths, physics, chemistry, computer an physical education be arranged so that physics and chemistry papers never come together.

Options

A. `54`
B. `120`
C. `48`
D. `72`

Explanation

To solve the problem of arranging five different examination papers (Math, Physics, Chemistry, Computer, and Physical Education) such that the Physics and Chemistry papers never come together, we can follow these steps:

### Step 1: Calculate the total arrangements of all papers
First, we calculate the total number of arrangements of the 5 different papers without any restrictions. This is given by the factorial of the number of papers.

\[ \text{Total arrangements} = 5! = 120 \]

### Step 2: Calculate the arrangements where Physics and Chemistry are together
Next, we treat the Physics and Chemistry papers as a single unit or block since we want to find the cases where they are together. This means we can consider the block (Physics + Chemistry) as one paper.

Now, we have the following blocks to arrange:
1. (Physics + Chemistry)
2. Math
3. Computer
4. Physical Education

This gives us a total of 4 blocks to arrange.

\[ \text{Arrangements of blocks} = 4! = 24 \]

### Step 3: Calculate the arrangements within the Physics and Chemistry block
Within the Physics and Chemistry block, we can arrange the two papers in 2 different ways (Physics first or Chemistry first).

\[ \text{Arrangements within the block} = 2! = 2 \]

### Step 4: Calculate the total arrangements where Physics and Chemistry are together
Now, we multiply the arrangements of the blocks by the arrangements within the Physics and Chemistry block:

\[ \text{Total arrangements with Physics and Chemistry together} = 4! \times 2! = 24 \times 2 = 48 \]

### Step 5: Calculate the arrangements where Physics and Chemistry are not together
To find the arrangements where Physics and Chemistry are not together, we subtract the arrangements where they are together from the total arrangements:

\[ \text{Arrangements where Physics and Chemistry are not together} = 5! - (4! \times 2!) = 120 - 48 = 72 \]

### Final Answer
Thus, the total number of ways to arrange the five examination papers such that Physics and Chemistry do not come together is:

\[ \boxed{72} \]