60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50ᵗʰ word is:

Solution

Maths sir · 3 steps

Count words in blocks by first letter until you reach 48, then list the last block one by one.

1. Order the letters. In alphabetical order the letters are B, B, H, J, O. The two B's are identical, so the total is 5!/2! = 60 words.

   First letter	Remaining letters	Number of words	Ranks covered
   B	B, H, J, O (all different)	4! = 24	1 to 24
   H	B, B, J, O	4!/2! = 12	25 to 36
   J	B, B, H, O	4!/2! = 12	37 to 48
   O	B, B, H, J	4!/2! = 12	49 to 60

2. Enter the O block. 48 words come before O, so the 50th word is the 2nd word that starts with O. In dictionary order the O block begins OBBHJ (49th), then OBBJH (50th).
3. So. The 50th word is OBBJH, which is option (a).

The idea to keep. To find the word at a given rank, count whole blocks of words by first letter, dividing by factorials for repeated letters. Then count one by one inside the block where the rank falls.

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