Arranging the letters of Allahabad with vowels at even places
To find the number of ways in which the letters of "Allahabad" can be arranged such that the vowels (A, A, A) occupy the even places, we can follow these steps:

Step 1: Identify the total number of ways to arrange all the letters
- The word "Allahabad" has 8 letters in total.
- Therefore, the total number of ways to arrange all the letters is 8!.

Step 2: Fix the positions of the vowels
- Since the vowels (A, A, A) must occupy the even places, we can fix them in those positions.
- There are 3 vowels to be placed in 4 even places (2nd, 4th, 6th, 8th).
- The number of ways to arrange the vowels in these positions is 4P3 = 4! / (4-3)! = 4!.

Step 3: Arrange the consonants
- After fixing the positions of the vowels, we are left with 5 consonants (L, L, H, B, D) and 4 odd places (1st, 3rd, 5th, 7th) to fill.
- The number of ways to arrange the consonants in these positions is 5P5 = 5! / (5-5)! = 5!.

Step 4: Calculate the total number of arrangements
- By multiplying the number of ways from Step 2 and Step 3, we get the total number of arrangements with vowels at even places: 4! * 5! = 2880.
Therefore, the letters of "Allahabad" can be arranged in 2880 ways such that the vowels (A, A, A) occupy the even places.