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 (Maths, 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 the 5 papers
The total number of ways to arrange 5 different papers 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
To find the arrangements where Physics and Chemistry are together, we can treat them as a single unit or block. This means we now have 4 units to arrange: (Physics-Chemistry), Maths, Computer, and Physical Education.

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

### Step 3: Arrange Physics and Chemistry within their block
Since Physics and Chemistry can be arranged among themselves, we need to multiply the arrangements of the 4 units by the arrangements of Physics and Chemistry.

\[ \text{Arrangements of Physics and Chemistry} = 2! = 2 \]

### Step 4: Calculate the total arrangements with Physics and Chemistry together
Now, we can find the total arrangements where Physics and Chemistry are together by multiplying the arrangements of the 4 units by the arrangements of Physics and Chemistry.

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

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

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

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

\[ \boxed{72} \]