The letters of the word MANKIND; are written in all possible orders and arranged in serial order as in an…

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 _____ .

Solution

M A N K I N D

Arranging the letters alphabetically, we get

ADIKMNN

When the word starts with any of the letters A/D/I/K, the number of possibilities=6!2!×4=1440

Now when the word starts with MA, then the number of possibilities=4!2!×3=36

Now when the word starts with MAN, then the number of possibilities=3!×2=12

Now when the word starts with MANK, then the number of possibilities=4

Hence, rank of the work MANKIND is 1492

Asked in: JEE Main 2022 (25 Jul Shift 1)

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