Question

If the letters of the word EAMCET are permuted in all possible ways and if the words thus formed are arranged in the dictonary krder, find the rank of the word. EAMCET​

Answer 1

Answer:

The required answer is $133$

Step-by-step explanation:

Think about the word EAMCET. The outcome of putting the letters in alphabetical order is ACEEMT. The dictionary's first entry will be this word. So long as A remains unchanged, the remaining letters can be rearranged in  $5!/2!$ or $60$ ways. With A remaining constant, the remaining letters can be rearranged in $5!/2!$ or $60$ different ways.

Let C be the first letter; the remaining letters can be placed in $5!/2!$ or $60$different ways.

If the initial letter is E, then EACEMT will be the first word in the dictionary that begins with E.  Let C be the third letter; the other three letters might be placed in $3!$ or $6$ different ways. The third letter, E, can be used in $6$ different ways. Let M be the third letter from now on, making EAMCET the first word.

Consequently, the word "EAMCET" will be ranked $60+60+6+6+1=120+12+1=133$

#SPJ3​