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If the letters of the word BAZAR are arranged in dictionary order, then what is the 50th word?
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The correct answer is:
$\quad$ ZAARB
With Aat first place, rest 4 places will be arranged in $4 !$ ways so, Number of words begin with $\mathrm{A}=4 !=24$ Similarly with $\mathrm{B}$ at first place,
Number of words begin with $\mathrm{B}=\frac{4 !}{2 !}=12$
[As there are two $\left.\mathrm{A}_{\mathrm{s}}\right]$
Number of words begin with $\mathrm{R}=\frac{4 !}{2 !}=12$
Thus, 48 words have starting letter $\mathrm{A}, \mathrm{B}$ and $\mathrm{R}$. So, 49 th word will be ZAABR and 50 th word will be ZAARB.
Number of words begin with $\mathrm{B}=\frac{4 !}{2 !}=12$
[As there are two $\left.\mathrm{A}_{\mathrm{s}}\right]$
Number of words begin with $\mathrm{R}=\frac{4 !}{2 !}=12$
Thus, 48 words have starting letter $\mathrm{A}, \mathrm{B}$ and $\mathrm{R}$. So, 49 th word will be ZAABR and 50 th word will be ZAARB.
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