<p>Two vowels are never together. In how many ways can we arrange them?</p>
Step-by-Step Solution
Key Concept: Arrange non-restricted items first, then place restricted items in available gaps to ensure they remain non-adjacent.
<p><strong>Step 1:</strong> This is a permutation problem where we need to arrange letters such that two specific vowels are never adjacent.</p><p><strong>Step 2:</strong> First arrange the consonants and other vowels, then place the two vowels in non-adjacent positions.</p><p><strong>Step 3:</strong> Using the standard approach of arranging 7 non-vowel items first (7! ways), then inserting 2 vowels in 8 available gaps with restriction.</p><p>∴ Answer is C: 220 × 7!</p>
Correct Answer: C