Question:
All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two $R$ appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is
Solution:
FARMER (6)
$\mathrm{A}, \mathrm{E}, \mathrm{F}, \mathrm{M}, \mathrm{R}, \mathrm{R}$
$\frac{\lfloor}{\lfloor 2}-4=60-24=36$
$\frac{\underline{3}}{L 2}-\lfloor 2=3-2=1$
$=1$
$=2$
$=1$
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77
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