All words, with or without meaning, are made using all the letters of the word MONDAY.

Question

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 :

Accepted Answer

The letters of "MONDAY" arranged in alphabetical order are: A, D, M, N, O, Y.

Fix A as the first letter, we can arrange the remaining 5 letters in 5! ways = 120 ways.
Fix D as the first letter, we can arrange the remaining 5 letters in 5! ways = 120 ways.

So far, we have 120 (for A) + 120 (for D) = 240 words.

Now, let\&\#39;s proceed with words starting with M:

Fix MA as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.
Fix MD as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.
Fix MN as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.

Now, we have 240 (for A and D) + 24 (for MA) + 24 (for MD) + 24 (for MN) = 312 words.

After MN, we consider words that start with MO:

Fix MOA as the first three letters, we can arrange the remaining 3 letters in 3! ways = 6 ways.
Fix MOD as the first three letters, we can arrange the remaining 3 letters in 3! ways = 6 ways.

Adding these to the total, we have 312 (previous total) + 6 (for MOA) + 6 (for MOD) = 324 words.

Next, we consider words that start with \&\#39;MON\&\#39;. The word \&\#39;MONDAY\&\#39; comes after \&\#39;MONAD\&\#39; in dictionary order, so:

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;.

So, we have 324 (previous total) + 2 (for \&\#39;MONADY\&\#39; and \&\#39;MONAYD\&\#39;) = 326 words.

Finally, we have the word \&\#39;MONDAY\&\#39; itself, which is the 327th word.

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