JEE MAIN - Mathematics (2023 - 6th April Evening Shift - No. 3)
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :
578
576
580
582
Explanation
Given word is PUBLIC.
Alphabetical order of letters is BCILPU. So, number of words start with letter.
B - - - - is $5 !=120$
C ---- is $5 !=120$
I ----- is $5 !=120$
$\mathrm{L}-----$ is $5 !=120$
$\mathrm{PB}----$ is $4 !=24$
$\mathrm{PC}----$ is $4 !=24$
PI ---- is $4 !=24$
$\mathrm{PL}----$ is $4 !=24$
PUBC -- is $2 !=2$
PUBI - is $2 !=2$
PUBLC - is $1 !=1$
PUBLIC is $0 !=1$
$\therefore$ Serial number of the word PUBLIC
$=4 \times 120+4 \times 24+2 \times 2+2 \times 1=582$
Alphabetical order of letters is BCILPU. So, number of words start with letter.
B - - - - is $5 !=120$
C ---- is $5 !=120$
I ----- is $5 !=120$
$\mathrm{L}-----$ is $5 !=120$
$\mathrm{PB}----$ is $4 !=24$
$\mathrm{PC}----$ is $4 !=24$
PI ---- is $4 !=24$
$\mathrm{PL}----$ is $4 !=24$
PUBC -- is $2 !=2$
PUBI - is $2 !=2$
PUBLC - is $1 !=1$
PUBLIC is $0 !=1$
$\therefore$ Serial number of the word PUBLIC
$=4 \times 120+4 \times 24+2 \times 2+2 \times 1=582$
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