Mathematics · Permutations and Combinations

JEE Main 2024 — 5 April, Shift 2 — Question 5

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

Answer: C

Word: $BHBJO$ $\Rightarrow$ Letters in order: $B,B,H,J,O$

Total words $=\frac{5!}{2!}=60$

Words starting with $B=4!=24$

Words starting with $H=\frac{4!}{2!}=12$

Words starting with $J=\frac{4!}{2!}=12$ Thus, words $1\text{–}48$ are before those starting with $O

50-48=2

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

2nd arrangement in order: $BBJH$

\boxed{\text{OBBJH}}

Answer key and solution verified before publishing.

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