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 :

Solution

Maths sir · 3 steps

Go letter by letter and count every word that comes before MONDAY, then add 1 for MONDAY itself.

1. Arrange alphabetically. The six letters are all different. In dictionary order they are A, D, M, N, O, Y.
2. Counting rule. At each position, look at the letters still unused. Every unused letter that is alphabetically smaller than the actual letter starts a block of words that come earlier. Each block has (letters left after it)! words.

   Fixed so far	Unused letters	Smaller than actual letter	Words skipped
   none (actual: M)	A, D, M, N, O, Y	A, D	2 × 5! = 240
   M (actual: O)	A, D, N, O, Y	A, D, N	3 × 4! = 72
   MO (actual: N)	A, D, N, Y	A, D	2 × 3! = 12
   MON (actual: D)	A, D, Y	A	1 × 2! = 2
   MOND (actual: A)	A, Y	none	0

   240 + 72 + 12 + 2 + 0 = 326

3. So. 326 words come before MONDAY, so MONDAY itself is word number 326 + 1 = 327, option (d).

The idea to keep. Rank of a word = (number of words that come before it) + 1. At each position, count only the unused letters smaller than the actual letter, and multiply by the factorial of the places left.

Answer from the NTA final answer key. Solution by PrepWiser.