JEE Main 2022 Mathematics question
The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is .
Answer: 1492
Solution
The letters in alphabetical order are A, D, I, K, M, N, N (N repeated). Words beginning with A, D, I or K: 6!/2! = 1440. Fix M, then A (no smaller letter): 0. Third letter N: the smaller remaining letters D, I, K give 4!/2! = 36. Fourth letter
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