Question

Seven person wearing medals with numbers 1, 2, 3, 4, 5, 6, 7 are seated on 7 chairs around a circular table. In how many ways can they be seated so that no two persons whose medals have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are considered different)

Answer 1

$\huge\red{Answer}$

➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️

☆☞ [ Verified answer ]☜☆

we know that no. of ways 'n' people can be seated around a round table =(n−1)!

∴ No. of ways '7' people can be seated around a round table =(7−1)!=6!=720

Now, no. of ways if two particular person (out of 7) sit together =5!×2=240

∴ No. of ways 7 people can be seated around a round table if two particular person can not sit together =720−240=480

Hence the correct answer is 480.

jai siya ram☺ __/\__

➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️➡️

¯\_(ツ)_/¯

Answer 2

719 or 720

Step-by-step explanation:

7-1 factorial as it is a circle. and in only one arrangement all are placed consecutively