Question

If a dictionary is made with the word 'ARYAN' . What will be the rank of the word 'ARYAN' in the dictionary ?

Answer 1

Given Word is ARYAN.

Assign the letters in alphabetical order and assign the values.

A R Y A N

1  3  4 1  2

(i) The digits which are less than 1 on right side= 0/2!(2 A's).

(ii) The digits which are less than 3 on right side = 2/0!. Here 2 = {1,2}

(iii) The digits which are less than 4 on right side = 2/0!.

(iv) The digits which are less than 1 on right side = 0/0!

(v) The digits which are less than 2 on right side = 0/0!.

Now,

Starting from right side, write 0!, 1!, 2!, 3!....

= > (0/0! * 0!) + (0/0! * 1!) + (2/0! * 2!) + (2/0! * 3!) + (0/2! * 4!)

We know that 0! = 1.

= > 0 + 0 + 4 + 12 + 0

= > 16.

Therefore, the rank of the word 'Aryan' = 16 + 1 = 17.

Hope it helps!