All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as in a dictionary. What will be the position of the word SACHIN in that sequence?
All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as in a dictionary. What will be the position of the word SACHIN in that sequence?
Explanation
601
If the word started with the latter A then the remaining 5 positions can be filled in 5! ways.
Similarly, for the other letters
No. of word starts with A = 5!
No. of word starts with C =5!
No. of word starts with H = 5!
No. of word starts with I = 5!
No. of word starts with N = 5!
Total words = 5! + 5! + 5! + 5! + 5! = 5(5!) = 600
Next when words starting with S appears, SACHIN itself will be the 1st word as ACHIN are all in dictionary order,
Now add the rank of SACHIN.
so rank is 600 + 1 = 601