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 $$50^{th}$$ word is :

We need to find the 50th word when all arrangements of the letters of BHBJO are written in dictionary order.

Letters of BHBJO: B, H, B, J, O — sorted in alphabetical order: B, B, H, J, O.

Total words = $$\frac{5!}{2!} = 60$$ (since B repeats twice).

Dictionary ordering — count words starting with each letter:

Words starting with B: Remaining letters are {B, H, J, O} (4 distinct). Number of arrangements = $$4! = 24$$. (Words 1-24)

Words starting with H: Remaining letters are {B, B, J, O}. Number of arrangements = $$\frac{4!}{2!} = 12$$. (Words 25-36)

Words starting with J: Remaining letters are {B, B, H, O}. Number of arrangements = $$\frac{4!}{2!} = 12$$. (Words 37-48)

Words starting with O: Remaining letters are {B, B, H, J}. Number of arrangements = $$\frac{4!}{2!} = 12$$. (Words 49-60)

The 50th word is the 2nd word among those starting with O.

Words starting with O, arranged in dictionary order:

Remaining letters: {B, B, H, J}, sorted: B, B, H, J.

Words starting with OB: Remaining {B, H, J} = $$3! = 6$$ words. (Words 49-54)

The 49th word is the first word starting with OB. Let's list:

- 49th: O B B H J

- 50th: O B B J H

So the 50th word is OBBJH.

The correct answer is Option (2): OBBJH.