<p>How many words can be formed using all the letters of the word <strong>BANANA</strong>?</p>
Step-by-Step Solution
Key Concept: When letters repeat, divide the total permutations by the factorial of each letter's frequency. Here, A appears 3 times and N appears 2 times, so use the formula n!/(n₁!×n₂!×...)
<p><strong>Step 1:</strong> Count total letters in BANANA: 6 letters total</p><p><strong>Step 2:</strong> Identify frequency of each letter:</p><ul><li>A appears 3 times</li><li>N appears 2 times</li><li>B appears 1 time</li></ul><p><strong>Step 3:</strong> Apply formula for permutations with repetition:</p><p>Number of words = n!/(n₁! × n₂! × n₃!)</p><p>= 6!/(3! × 2! × 1!)</p><p><strong>Step 4:</strong> Calculate:</p><p>= 720/(6 × 2 × 1)</p><p>= 720/12</p><p>= 60</p><p>∴ Answer: <strong>60</strong></p>
Correct Answer: 60