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

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

To find the position of MONDAY, we count how many words come before it in dictionary order.

Words starting with A or D (before M): $$2 \times 5! = 2 \times 120 = 240$$

Words starting with M, then a letter before O (i.e., MA..., MD..., MN...): $$3 \times 4! = 3 \times 24 = 72$$

Words starting with MO, then a letter before N (i.e., MOA..., MOD...): $$2 \times 3! = 2 \times 6 = 12$$

Words starting with MON, then a letter before D (i.e., MONA...): $$1 \times 2! = 2$$

Words starting with MOND, then a letter before A: none, since A is the smallest remaining letter. So $$0$$.

MONDAY itself is the next word: $$+1$$

Total position = $$240 + 72 + 12 + 2 + 0 + 1 = 327$$