How many different words can be formed with the letters of the word ‘JAIPUR’ which start with ‘A’ and end with ‘I’?

Options

A. A) 20
B. B) 18
C. C) 720
D. D) 24

Answer

To solve the problem of how many different words can be formed with the letters of the word ‘JAIPUR’ that start with ‘A’ and end with ‘I’, we can follow these steps:

### Step 1: Identify the fixed letters
We know that the word must start with 'A' and end with 'I'. Therefore, we can fix 'A' at the beginning and 'I' at the end of the arrangement.

**Hint:** When certain positions in a permutation are fixed, it simplifies the problem by reducing the number of letters to arrange.

### Step 2: Count the remaining letters
After fixing 'A' and 'I', we are left with the letters 'J', 'P', 'U', and 'R'. This gives us a total of 4 letters to arrange.

**Hint:** Always count how many items are left after fixing certain positions.

### Step 3: Calculate the arrangements of the remaining letters
The number of ways to arrange 'J', 'P', 'U', and 'R' can be calculated using the factorial of the number of letters we have left. Since we have 4 letters, the number of arrangements is given by 4! (4 factorial).

**Hint:** The factorial of a number n (denoted as n!) is the product of all positive integers up to n.

### Step 4: Compute the factorial
Now, we calculate 4!:
\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \]

**Hint:** Remember that factorials grow quickly, so it’s useful to memorize small factorials.

### Step 5: Conclusion
Thus, the total number of different words that can be formed with the letters of the word ‘JAIPUR’ starting with 'A' and ending with 'I' is 24.

**Final Answer:** 24