Possible Permutations

To find the rank of the word 'SURITI' when its letters are arranged in all possible orders, we need to determine the position of the word in a dictionary. Let's break down the process step by step:

1. Identify the total number of permutations
- The word 'SURITI' consists of 6 letters.
- Therefore, the total number of permutations can be calculated as 6! (factorial), which is equal to 720.

2. Sort the letters alphabetically
- To determine the rank of the word 'SURITI', we need to sort the letters alphabetically.
- The sorted form of 'SURITI' is 'IIRSTU'.

3. Count the number of words starting with each letter
- We count the number of words that can be formed using the remaining 5 letters (excluding 'I') in alphabetical order.
- The number of words starting with 'I' can be calculated as 5! (factorial), which is equal to 120.

4. Calculate the rank within each letter group
- Within the letter group starting with 'I', we need to determine the rank of the word 'SURITI'.
- We compare each letter of 'IIRSTU' with the corresponding letter of 'SURITI' from left to right.
- If the letters are the same, we move to the next letter.
- If the letters are different, we calculate the number of words that can be formed with the remaining letters in alphabetical order.
- For example, in the first position, 'I' is the same in both words, so we move to the next position.
- In the second position, 'I' is different from 'U', so we calculate the number of words starting with 'I' in alphabetical order, which is 3! (factorial), equal to 6.
- Continuing this process, we find that the rank within the letter group starting with 'I' is 6.

5. Calculate the rank of the word 'SURITI'
- To calculate the final rank, we need to add the ranks from all the previous letter groups.
- In this case, there are no letter groups before 'I', so the rank of 'SURITI' will be the same as the rank within the letter group starting with 'I', which is 6.

Rank of the word 'SURITI': 6