18 If the different permutations of the word ATLANTIC are listed as in a dictionary, how many items - Maths - Permutations and Combinations

Question

18 If the different permutations of the word ATLANTIC are listed as
in a dictionary, how many items are there in the list before the
first word starting with I?

Aarushi Mishra · Accepted Answer

Put A in first place
 We are left with1- A's2-T's1- L's1- N's1- I's1- C'sTotal 7 letters, Number of arrangements of 7 letters at 7 places of which 2 are identical=7!2!Put C in first place
 We are left with2- A's2-T's1- L's1- N's1- I's0- C'sTotal 7 letters, Number of arrangements of 7 letters at 7 places of which 2 are are identical of one kind and 2 are identical but of other kind=7!2!2!Next set of words will start with I
So number of words before the first word that starts with I=7!2!+7!2!2!=3780

18. If the different permutations of the word ATLANTIC are listed as in a dictionary, how many items are there in the list before the first word starting with I?