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QJEEM23Ma9a57: JEE Main 2023 Mathematics - Class 11 JEEM23Ma9a57 Solution: All the letters of the word PUBLIC are written in all possible…

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 :

Multiple Choice Options

  • A 578
  • B 576
  • C 580
  • D 582

Step-by-Step Verified Solution

Given word is PUBLIC.

Alphabetical order of letters is BCILPU. So, number of words start with letter.

B - - - - is 5!=1205 !=120

C ---- is 5!=1205 !=120

I ----- is 5!=1205 !=120

L−−−−−\mathrm{L}----- is 5!=1205 !=120

PB−−−−\mathrm{PB}---- is 4!=244 !=24

PC−−−−\mathrm{PC}---- is 4!=244 !=24

PI ---- is 4!=244 !=24

PL−−−−\mathrm{PL}---- is 4!=244 !=24

PUBC -- is 2!=22 !=2

PUBI - is 2!=22 !=2

PUBLC - is 1!=11 !=1

PUBLIC is 0!=10 !=1

∴\therefore Serial number of the word PUBLIC

=4×120+4×24+2×2+2×1=582=4 \times 120+4 \times 24+2 \times 2+2 \times 1=582

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