Permutations & Combinations
Grade None
Question:
<p>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</p>
<p style="display:inline">576</p>
<p style="display:inline">580</p>
<p style="display:inline">578</p>
<p style="display:inline">582</p>
Step-by-Step Solution
Key Concept: The dictionary rank of a word is calculated by systematically summing the permutations of all possible words that appear alphabetically before the target word by fixing characters position by position.
<p>Since B ... <span class="math-tex">$\rightarrow$</span> 5! = 120<br />
C ... <span class="math-tex">$\rightarrow$</span> 5! = 120<br />
I ... <span class="math-tex">$\rightarrow$</span> 5! = 120<br />
L ... <span class="math-tex">$\rightarrow$</span> 5! = 120<br />
PB ... <span class="math-tex">$\rightarrow$</span> 4! = 24<br />
PC ... <span class="math-tex">$\rightarrow$</span> 4! = 24<br />
PL ... <span class="math-tex">$\rightarrow$</span> 4! = 24<br />
PI ... <span class="math-tex">$\rightarrow$</span> 4! = 24<br />
PUBC ... <span class="math-tex">$\rightarrow$</span> 2! = 2<br />
PUBI ... <span class="math-tex">$\rightarrow$</span> 2! = 2<br />
PUBLC ... <span class="math-tex">$\rightarrow$</span> 1! = 1<br />
PUBLIC ... <span class="math-tex">$\rightarrow$</span><strong> </strong>= 1<br />
Serial number = 4(120) + 4(24) + 6 = 582</p>
Correct Answer: D