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# Two Arrangements | PRMO 2019 | Question 5

Try this beautiful problem from the Pre-RMO, 2019 based on Two Arrangements. You may use sequential hints to solve the problem.

Try this beautiful problem from the PRMO, 2019 based on Two arrangements.

## Two arrangements – PRMO 2019

Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a circular table. Find the number of ways they be seated that no two persons whose badges have consecutive numbers are seated next to each other.

• is 107
• is 10
• is 840
• cannot be determined from the given information

### Key Concepts

Arrangement

Algebra

Number Theory

PRMO, 2019, Question 5

Combinatorics by Brualdi

## Try with Hints

First hint

Here they may seat in circular way such that 1,3,5,2,4 and again 1

Second Hint

then they may seat in another circular way 1,4,2,5,3 and again 1

Final Step

Then number of ways = (2)(5) =10.

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