First slide

Permutations

Question

If all permutations of the letters of the word P E N C I L are arranged as in a dictionary, then 413th word is

Moderate

A

L I C N E P
B

L I C N P E
C

L I C P N E
D

L I C P E N

Solution

Letters in the word PENCIL are C, E, I, L, N, P.
There are $5!$ words each beginning with C, E and I. That is, there are $3 (5!) = 360$
words beginning with C, E, I Words beginning with L have serial numbers 361 to 480 $4! = 24$
words beginning with LC have serial numbers 36 to 384.
Words beginning with LE are numbered from 385 to 408.
Words beginning with LIC are numbered from 409 to 414.
Now 414th word is L I C P N E and $413^{th}$ word is L I C P E N.

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