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

1. Fix A as the first letter, we can arrange the remaining 5 letters in 5! ways = 120 ways.
2. 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's proceed with words starting with M:

1. Fix MA as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.
2. Fix MD as the first two letters, we can arrange the remaining 4 letters in 4! ways = 24 ways.
3. 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:

1. Fix MOA as the first three letters, we can arrange the remaining 3 letters in 3! ways = 6 ways.
2. 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 'MON'. The word 'MONDAY' comes after 'MONAD' in dictionary order, so:

1. Fix 'MONA' as the first four letters. The remaining 2 letters ('D' and 'Y') can be arranged in 2! ways, which gives us 2 more words: 'MONADY' and 'MONAYD'.

So, we have 324 (previous total) + 2 (for 'MONADY' and 'MONAYD') = 326 words.

Finally, we have the word 'MONDAY' itself, which is the 327th word.