Calculation of the Rank of a Word in Alphabetical Order
<p>There are 5 letters in the word "RACHIT" of which "R" comes last alphabetically. We can find the rank by finding the number of words that can be formed with each of the preceding alphabets as the first letter and summing them up, then adding 1 for the given word itself.</p>
<p>If "A" is the first letter, the remaining letters can be arranged in 4! ways.</p>
<p>If "C" is the first letter, the remaining letters can be arranged in 4! ways.</p>
<p>If "H" is the first letter, the remaining letters can be arranged in 4! ways.</p>
<p>If "I" is the first letter, the remaining letters including one "R" can be arranged in 4! ways.</p>
<p>When "R" is the starting letter, all previous permutations are sorted before the given word, "RACHIT".</p>
<p>Now, to find the sum:</p>
<p>Rank = 4! + 4! + 4! + 4!</p>
<p>Rank = 4(4!)</p>
<p>Rank = 4(24)</p>
<p>Rank = 96</p>
<p>The rank of the word "RACHIT" is the sum found plus 1 for the word itself, meaning the final rank is 96 + 1.</p>
<p>Rank = 97</p>
