All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :

<p>The letters of &quot;MONDAY&quot; arranged in alphabetical order are: A, D, M, N, O, Y.</p> <ol> <li>Fix A as the first letter, we can arrange the remaining 5 letters in 5! ways = 120 ways.</li> <li>Fix D as the first letter, we can arrange the remaining 5 letters in 5! ways = 120 ways.</li> </ol> <p>So far, we have 120 (for A) + 120 (for D) = 240 words.</p> <p>Now, let&#39;s proceed with words starting with M:</p> <ol> <li>Fix MA as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.</li> <li>Fix MD as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.</li> <li>Fix MN as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.</li> </ol> <p>Now, we have 240 (for A and D) + 24 (for MA) + 24 (for MD) + 24 (for MN) = 312 words.</p> <p>After MN, we consider words that start with MO:</p> <ol> <li>Fix MOA as the first three letters, we can arrange the remaining 3 letters in 3! ways = 6 ways.</li> <li>Fix MOD as the first three letters, we can arrange the remaining 3 letters in 3! ways = 6 ways.</li> </ol> <p>Adding these to the total, we have 312 (previous total) + 6 (for MOA) + 6 (for MOD) = 324 words.</p> <p>Next, we consider words that start with &#39;MON&#39;. The word &#39;MONDAY&#39; comes after &#39;MONAD&#39; in dictionary order, so:</p> <ol> <li>Fix &#39;MONA&#39; as the first four letters. The remaining 2 letters (&#39;D&#39; and &#39;Y&#39;) can be arranged in 2! ways, which gives us 2 more words: &#39;MONADY&#39; and &#39;MONAYD&#39;.</li> </ol> <p>So, we have 324 (previous total) + 2 (for &#39;MONADY&#39; and &#39;MONAYD&#39;) = 326 words.</p> <p>Finally, we have the word &#39;MONDAY&#39; itself, which is the 327th word. </p>