If a dictionary is formed with the words formed using the letters of the word SMART and are arranged in alphabetical sequence, then what is the rank of the word SMART in it?

To find the rank of the word SMART in the dictionary formed by arranging the words formed using the letters of the word SMART in alphabetical sequence, we can follow these steps:

1. Start by arranging the letters of the word SMART in alphabetical order. In this case, the letters are already in alphabetical order, so we have the word SMART.

2. Now, we need to find all the possible permutations of the letters in the word SMART. These permutations will give us all the words that can be formed using the letters of the word SMART.

3. Arrange these words in alphabetical order. Since the word SMART is already in alphabetical order, it will be the first word in the list.

4. The rank of the word SMART in the dictionary will be the position of the word SMART in the list of all the words formed using the letters of the word SMART, arranged in alphabetical order.

So, the rank of the word SMART in the dictionary formed by arranging the words formed using the letters of the word SMART in alphabetical sequence is 1.

To find the rank of the word SMART in the dictionary formed by arranging the words formed using the letters of the word SMART in alphabetical sequence, we can follow these steps:

1. Start by arranging the letters of the word SMART in alphabetical order, which gives us the word AMRST.

2. Now, we need to find all the possible permutations of the letters in the word AMRST. This can be done by using a permutation formula, which is given by n! / (n1! * n2! * ... * nk!), where n is the total number of letters and n1, n2, ..., nk are the frequencies of each letter.

In this case, we have 5 letters in total, so n = 5. Since all the letters in the word AMRST are unique, the frequencies of each letter are all 1. Therefore, the formula simplifies to 5! / (1! * 1! * 1! * 1! * 1!) = 5! = 120.

This means that there are 120 possible permutations of the letters in the word AMRST.

3. Next, we need to arrange these permutations in alphabetical order. To do this, we can use a sorting algorithm or manually sort them.

After sorting the permutations, we can find the rank of the word SMART by locating it in the sorted list. The position of the word SMART in the sorted list will be its rank.

Please note that manually calculating the rank for a large number of permutations can be time-consuming. In such cases, it is recommended to use a computer program or algorithm to find the rank efficiently.