Permutations & Combinations
Arrangements with Constraints
Grade 11

Question:

<p>If a vowel appears in between two similar letters, the number of simple words is</p>
<p>(a) 12</p>
<p>(b) 6</p>
<p>(c) 36</p>
<p>(d) 14</p>

Step-by-Step Solution

Key Concept: Identify when vowels must appear between the two similar letters and count valid arrangements considering the constraint.
<p><strong>Solution:</strong> The word 'AGAIN' has letters A, G, A, I, N with two A's (similar letters).</p><p>When a vowel appears between two similar A's: A-vowel-A</p><p>We can arrange these as: (A-I-A), G, N</p><p>Number of arrangements = $3! / 1 = 6$</p><p>∴ Answer is (b) 6</p>
Correct Answer: b

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