Let’s solve this step by step in a simple way! 🎉

We need to arrange the letters of DETAIL so that vowels (E, A, I) only occupy the odd positions. ✅

Step 1: Identify vowels and consonants 🔤
The word DETAIL has 6 letters:

• Vowels (🟢): E, A, I
• Consonants (🔵): D, T, L

Step 2: Identify available positions 📍
Since there are 6 positions in total, the odd positions are:
1, 3, 5

The even positions are:
2, 4, 6

We must place the vowels (E, A, I) in the odd positions and the consonants (D, T, L) in the even positions.

Step 3: Arrange the vowels in odd positions 🔢
There are 3 vowels (E, A, I) to be placed in 3 odd positions.
They can be arranged among themselves in:

3!=3×2×1=63! = 3 \times 2 \times 1 = 6

Step 4: Arrange the consonants in even positions 🔄
There are 3 consonants (D, T, L) to be placed in 3 even positions.
They can be arranged among themselves in:

3!=3×2×1=63! = 3 \times 2 \times 1 = 6

Step 5: Multiply both arrangements ✖️
Since the vowel and consonant arrangements are independent, we multiply them:

6×6=366 \times 6 = 36

🎯 Final Answer:
The letters of DETAIL can be arranged in 36 ways while keeping vowels in odd positions! 🎊😊