Question

If the letters of the word EAMCET are permuted in all possible ways and if the word thus formed are arranged in dictionary order , find the rank of the word EAMCET .

Answer 1

Before $E$ there will be the words starting with $A$

No of words starting with $A$ is $\frac{5!}{2!}=60$

Now Fix the first letter as $E$

Remaining letters will be $A,C,E,M,T$

There is no chance for second letter other than $A$

So fix the second letter as $A$

Before $M$ there is chance for $C,E$

No of words with third letter as $C,E$ is $2\times 3!=12$

Fix the third letter as $M$

there is no chance for fourth letter other than $C$

Similarly for fifth and sixth letter too
So Rank of the word $EAMCET$ is $60+12+1=73$