JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q22

← JEE Main 2022 · 25 Jul · Shift 1

MathematicsInteger+4 / -1Question 22 of 90

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 ______.

Your answer

Answer and worked solution

Official answer: 1492

Letters A, D, I, K, M, N, N.

Count words before MANKIND. Starting A, D, I or K: $4\times\frac{6!}{2!}=1440$ . MA then D, I or K: $3\times\frac{4!}{2!}=36$ . MAN then D or I: $2\times3!=12$ . MANK then D: $2!=2$ . MANKI then D: 1. Total 1491.

Rank 1492.

Answer: 1492

Topics:Permutations

← Previous question Next question →

JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 22