Formation of 4-letter words using the letters of the word "gujrat"

To determine the number of 4-letter words that can be formed using the letters of the word "gujrat," we need to consider the following:

1. Total number of letters:
The word "gujrat" has a total of 6 letters.

2. Repetition of letters:
The word "gujrat" has 2 repeated letters, 'g' and 'r'.

3. Permutations:
Permutation refers to the arrangement of objects in a particular order. In this case, we need to find the number of arrangements of 4 letters taken from a set of 6 letters.

4. Use of nPr formula:
The formula to calculate the number of permutations is given by nPr = n! / (n-r)!, where n represents the total number of objects and r represents the number of objects taken at a time.

Now, let's calculate the number of 4-letter words that can be formed using the letters of the word "gujrat" by following these steps:

Step 1: Identify the distinct letters in the word "gujrat."
In this case, the distinct letters are 'g', 'u', 'j', 'r', 'a', and 't'.

Step 2: Calculate the number of arrangements of 4 letters taken from the set of distinct letters.
Using the nPr formula, we have: nPr = 6! / (6-4)! = 6! / 2! = 6 x 5 x 4 x 3 = 360.

Therefore, there are a total of 360 different 4-letter words that can be formed using the letters of the word "gujrat."