All the letters of the word PUBLIC are written in all possible orders and these words are …

Question

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 :

Accepted Answer

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 $0 !=1$

$	herefore$ Serial number of the word PUBLIC

$=4 	imes 120+4 	imes 24+2 	imes 2+2 	imes 1=582$

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