Question

The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary, then the rank of the word MODESTY is

Answer 1

Rank of the word MODESTY is 1681

Step-by-step explanation:

MODESTY

Total letters are 7

• First arrange letters in alphabetical order

               D E M O S  T Y

• Words start with D are

               D _ _ _ _ _ _ = 6! = 720

• Words start with E are

               E _ _ _ _ _ _   = 6! = 720

• Now we can see that in word MODESTY letter D and E  Counted

• Word start with MD are

               MD _ _ _ _ _  =  5 ! = 120

• Word start with ME

              ME _ _ _ _ _  =  5 ! = 120

Now the first word starts with MO is nothing but MODESTY

Hence, Rank of MODESTY  720 + 720 + 120 + 120 = 1681

Thus, The rank of word MODESTY is 1681