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 :
Solution
Given word is PUBLIC.
<br/><br/>Alphabetical order of letters is BCILPU. So, number of words start with letter.
<br/><br/>B - - - - is $5 !=120$
<br/><br/>C ---- is $5 !=120$
<br/><br/>I ----- is $5 !=120$
<br/><br/>$\mathrm{L}-----$ is $5 !=120$
<br/><br/>$\mathrm{PB}----$ is $4 !=24$
<br/><br/>$\mathrm{PC}----$ is $4 !=24$
<br/><br/>PI ---- is $4 !=24$
<br/><br/>$\mathrm{PL}----$ is $4 !=24$
<br/><br/>PUBC -- is $2 !=2$
<br/><br/>PUBI - is $2 !=2$
<br/><br/>PUBLC - is $1 !=1$
<br/><br/>PUBLIC is $0 !=1$
<br/><br/>$\therefore$ Serial number of the word PUBLIC
<br/><br/>$=4 \times 120+4 \times 24+2 \times 2+2 \times 1=582$
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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