Explanation:

To find the number of words that appear before the word "RADHIKA" when the letters of the word are arranged in alphabetical order, we need to consider the permutations of the letters in the word.

Step 1: Finding the number of permutations

The word "RADHIKA" has 7 letters, so the number of permutations of these letters is given by 7!.

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

Step 2: Finding the number of permutations starting with each letter

Since we want to find the number of words that appear before "RADHIKA" in alphabetical order, we need to consider the permutations of the letters that come before 'R' in the alphabet.

There are 17 letters before 'R' in the alphabet (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q), so for each of these letters, we can arrange the remaining 6 letters (A, D, H, I, K, A) in 6! ways.

Therefore, the number of permutations starting with each letter before 'R' is given by 17 x 6!

17 x 6! = 17 x 6 x 5 x 4 x 3 x 2 x 1 = 12,240

Step 3: Finding the number of permutations starting with 'RA'

Next, we need to consider the permutations starting with 'RA'. Since 'A' is repeated twice in the word, we need to divide the total number of permutations starting with 'RA' by 2 to account for the repetition.

The number of permutations starting with 'RA' is given by 6! / 2!

6! / 2! = (6 x 5 x 4 x 3 x 2 x 1) / (2 x 1) = 360

Step 4: Finding the number of permutations starting with 'RAD'

Similarly, we need to consider the permutations starting with 'RAD'. Since 'A' is repeated twice in the word, we need to divide the total number of permutations starting with 'RAD' by 2 to account for the repetition.

The number of permutations starting with 'RAD' is given by 5! / 2!

5! / 2! = (5 x 4 x 3 x 2 x 1) / (2 x 1) = 60

Step 5: Finding the number of permutations starting with 'RADH'

Following the same logic as above, the number of permutations starting with 'RADH' is given by 4! / 2!

4! / 2! = (4 x 3 x 2 x 1) / (2 x 1) = 12

Step 6: Finding the number of permutations starting with 'RADHI'

The number of permutations starting with 'RADHI' is given by 3! = 3 x 2 x 1 = 6.

Step 7: Finding the number of permutations starting with 'RADHIK'

The number of permutations starting with 'RADHIK