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Visual SolutionPYQ 2023 · Apr 6 Shift 2Standard

Question

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

(A)

576

(B)

578

(C)

580

(D)

582

Solution Path

Dictionary rank:

4 \times 5! + 4 \times 4! + 2 \times 2! + 1 + 1 = 582

01Question Setup

1/4

Find the rank of the word PUBLIC in dictionary ordering of all its letters.

\text{Rank} = \;?

02Alphabetical Order

2/4

Letters in order: B, C, I, L, P, U. Count words before PUBLIC systematically.

B, C, I, L, P, U

03Count RankKEY INSIGHT

3/4

Words before:

4 \times 5! + 4 \times 4! + 2 \times 2! + 1 = 480 + 96 + 4 + 1

. Add 1 for PUBLIC itself:

582

480 + 96 + 4 + 1 + 1 = 582

04Final Answer

4/4

Rank of PUBLIC

= 582

\boxed{582}

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