Problem: In how many ways can the letter sandesh be arranged so that the vowels occupy the even places?

Solution:
To solve this problem, we need to follow the steps given below:

Step 1: Count the number of vowels in the given word.
In the given word 'sandesh', there are two vowels 'a' and 'e'.

Step 2: Count the number of even positions.
In a word of length 'n', there are n/2 even positions.

In the given word 'sandesh', there are 6 even positions, which are 2nd, 4th, 6th, 8th, 10th, and 12th.

Step 3: Fix the vowels in the even positions.
Since there are two vowels and six even positions, we need to choose two positions for the vowels and fix them.

The first vowel can be fixed in any of the three even positions (2nd, 4th or 6th), and the second vowel can be fixed in any of the remaining two even positions.

Therefore, the number of ways to fix the vowels in the even positions is:

3C1 x 2C1 = 6

Step 4: Arrange the consonants in the odd positions.
The remaining consonants can be arranged in the odd positions in (4!) ways.

Step 5: Find the total number of arrangements.
Using the multiplication principle, the total number of arrangements is:

6 x 4! = 144

Therefore, there are 144 ways to arrange the letters of the word 'sandesh' such that the vowels occupy the even places.