Discussion Problem_(19)

[duck]

1) Suppose, there are 20 people among whom are 2 brothers. Find the number of ways in which these people can be arranged in a CIRCLE such that there is exactly on person between the two brother.

[diptendra1991]

(2)(18!)

[MI]

2 (17!)

[Mauli]

2!17!

[Sinistral]

17! * (18C2 * 2!)

[Akshay Jain]

select a person that will sit b/w the brothers in 18c1=18 ways
make that person sit in between and den the brothers cn be arranged in 2 ways
no of groups that can be formed is 18*2
now treat dis grup as 1 indivisual and there are other 17 indivisuals so total is 18
no of circular arrangements is 17!
total possible arrangements is 18*2*17!=2*18!

[Sumit]

18*2*17!..

[Sinistral]

oh.. i made a mistake earlier. I calculated for "2 brothers cant sit together" rather than calculating for "exactly one person has to sit in between those 2 brothers".

and yes..  the answer should be: 18C1 *2 * 17!

[Mauli]

thanks akshay:)
ur explanation made it quite clear where i was going wrong.

[duck]

Great guys.. :)

Correct Answer: 18C1*2*17!