<p>Total number of words that can be formed using all letters of the word BRIJESH that neither begins with I nor ends with B is equal to</p>
Step-by-Step Solution
Key Concept: Use complementary counting: Total arrangements minus (arrangements beginning with I + arrangements ending with B - arrangements both beginning with I AND ending with B). This avoids overcounting restrictions.
<p><strong>Step 1:</strong> Count total arrangements of BRIJESH.</p><p>BRIJESH has 7 distinct letters, so total arrangements = 7! = 5040</p><p><strong>Step 2:</strong> Count arrangements beginning with I.</p><p>Fix I at first position, arrange remaining 6 letters = 6! = 720</p><p><strong>Step 3:</strong> Count arrangements ending with B.</p><p>Fix B at last position, arrange remaining 6 letters = 6! = 720</p><p><strong>Step 4:</strong> Count arrangements both beginning with I AND ending with B.</p><p>Fix I at first, B at last, arrange remaining 5 letters = 5! = 120</p><p><strong>Step 5:</strong> Apply inclusion-exclusion principle.</p><p>Arrangements beginning with I OR ending with B = 720 + 720 - 120 = 1320</p><p><strong>Step 6:</strong> Apply complementary counting.</p><p>Arrangements neither beginning with I nor ending with B = 5040 - 1320 = 3720</p><p>∴ Answer: A</p>
Correct Answer: A