Question

If all the words that are formed by permuting the letters of the word ${}^{\prime }PLAT{E}^{\prime }$ are arranged in alphabetical order, then the rank of the word ${}^{\prime }PLAT{E}^{\prime }$ is

• A. $81$
• B. $86$
• C. $80$
• D. $85$

Answer 1

The correct option is B $86$

First number of all the words starting with $A=4!$
Starting with $E=4!$
Starting with $L=4!$
Starting with $PA=3!$
Starting with $PE=3!$

Starting with $PLA=2!$ i.e. Next words are $PLAET$ and $PLATE$

So rank of the given word $=3\times 4!+2\times 3!+2!=86$