Permutations And Combinations

The given word is "COCHIN". We need to find how many words appear before "COCHIN" when all permutations of the letters are arranged in alphabetical order.
The letters of the word "COCHIN" in alphabetical order are: . 1. First letter: The first letter in "COCHIN" is , and the words starting with and will precede it.
Since there are no 's or 's in the word, we move to the next letter. 2. Second letter: The second letter in "COCHIN" is . So, we will find all permutations where the first letter is , but the second letter is less than . - If the second letter is , the possible remaining letters are: . The number of permutations of these 4 letters is: 3. Third letter: The third letter in "COCHIN" is . Now, we find the permutations where the first two letters are and , but the third letter is less than . - If the third letter is , the remaining letters are , so the number of permutations of these two letters is: Thus, the total number of permutations that appear before "COCHIN" is:

The candidate has to select 7 questions with at least 2 from each group.
Hence, the selection should be made as follows:
- From group A, select 2 questions (since at least 2 questions need to be selected).
- From group B, select 2 questions (since at least 2 questions need to be selected).
- From group C, select 3 questions (since 7 questions need to be selected in total).
The number of ways to select the questions from each group is given by the combination formula , where is the total number of questions in the group, and is the number of questions to be selected. For group A (4 questions, 2 to be selected): For group B (5 questions, 2 to be selected): For group C (6 questions, 3 to be selected): Now, multiply the number of ways to select questions from each group: Thus, the correct answer is 2700.