1. Arrange the letters in dictionary order

The letters of the word $\mathrm{BHBJO}$ are: $B, B, H, J, O$

In alphabetical order: $B < H < J < O$

Since there are 5 letters with 2 identical $B$'s, the total number of distinct words is $\frac{5!}{2!} = 60$ which matches the question.

2. Find the 50th word lexicographically

We count how many words begin with each possible first letter.

Case 1: First letter $B$

Remaining letters: $B,H,J,O$

Number of words: $\frac{4!}{1!}=24$ So words numbered $1$ to $24$ start with $B$.

Case 2: First letter $H$

Remaining letters: $B,B,J,O$

Number of words: $\frac{4!}{2!}=12$ So words numbered $25$ to $36$ start with $H$.

Case 3: First letter $J$

Remaining letters: $B,B,H,O$

Number of words: $\frac{4!}{2!}=12$ So words numbered $37$ to $48$ start with $J$.

Case 4: First letter $O$

Remaining letters: $B,B,H,J$

Number of words: $\frac{4!}{2!}=12$ So words numbered $49$ to $60$ start with $O$.

Therefore, the $50^{\text{th}}$ word is the 2nd word among those starting with $O$.

3. Now list words starting with $O$

We need the 2nd arrangement of the multiset $B,B,H,J$ in dictionary order.

All distinct arrangements of $B,B,H,J$ in lexicographic order begin as:

1. $BBHJ$
2. $BBJH$
3. $BHBJ$
4. $BHJB$
5. $BJBH$
6. $BJHB$
7. $HBBJ$
8. $HBJB$
9. $HJBB$
10. $JBBH$
11. $JBHB$
12. $JHBB$

Thus, the 2nd word beginning with $O$ is: $OBBJH$

4. Match with options

$OBBJH$ corresponds to Option C.

5. Compare with stored correct answer

Stored correct answer is A: OBBJH. But option A is written as $\text{OBBJH}$? Let's check the listed options:

• A: $\text{OBBJH}$
• C: $\text{OBBHJ}$

So the derived answer is A, not C.

Therefore, the correct option is A.