Total no of ways six mobsters will be arranged = 6! = 720

Half of the times Joey will be ahead of Frankie and half of the times Frankie will be ahead of Joey.

So 360 is the answer.

Method -II

J - - - - - = 5C1( Frankie can take any of the 5 places) * 4!( remaining people can be arranged ) = 5 *4!
- J - - - - = 4 * 4!
so on

= (5 + 4 + 3 + 2 + 1) * 4! = 360

Thanks,
Raama

thanks Raama!!!

krisraam wrote:Total no of ways six mobsters will be arranged = 6! = 720

Half of the times Joey will be ahead of Frankie and half of the times Frankie will be ahead of Joey.

So 360 is the answer.

Method -II

J - - - - - = 5C1( Frankie can take any of the 5 places) * 4!( remaining people can be arranged ) = 5 *4!
- J - - - - = 4 * 4!
so on

= (5 + 4 + 3 + 2 + 1) * 4! = 360

Thanks,
Raama

Raama,
The logic makes sense; however, can you tell if this makes sense? I did it in a way by considering the Joey, Frankie as a pair who can be arranged in 3 ways and I get the same result! I am doubting the solution because I cannot take Joey/Frankie as a pair. The stimulus explicitly tells Joey and Frankie cannot stand next to each other!!

Soln:
- - - - - -
J F

Taking J/F next to each other we have 5!

Now J/F can be arranged as a pair in 3 ways:
- - J F - -
- - - - J F
J F - - - -
Hence, 3 * 5! = 3 * 120 = 360

Please, any help to make my understanding clearer is appreciated!

kanha81 wrote:

krisraam wrote:Total no of ways six mobsters will be arranged = 6! = 720

Half of the times Joey will be ahead of Frankie and half of the times Frankie will be ahead of Joey.

So 360 is the answer.

Method -II

J - - - - - = 5C1( Frankie can take any of the 5 places) * 4!( remaining people can be arranged ) = 5 *4!
- J - - - - = 4 * 4!
so on

= (5 + 4 + 3 + 2 + 1) * 4! = 360

Thanks,
Raama

Raama,
The logic makes sense; however, can you tell if this makes sense? I did it in a way by considering the Joey, Frankie as a pair who can be arranged in 3 ways and I get the same result! I am doubting the solution because I cannot take Joey/Frankie as a pair. The stimulus explicitly tells Joey and Frankie cannot stand next to each other!!

Soln:
- - - - - -
J F

Taking J/F next to each other we have 5!

Now J/F can be arranged as a pair in 3 ways:
- - J F - -
- - - - J F
J F - - - -
Hence, 3 * 5! = 3 * 120 = 360

Please, any help to make my understanding clearer is appreciated!

The Stimulus says Frankie wants to stand behind Joey not necessarily right behind. This means Frankie can stand any where as long as Joey is ahead of him.

If J/F is taken as a pair the total arrangements are 5! = 120. (Joey and Frankie can't be arranged among themselves in the group). This covers all the arrangements where J/F are together and Joey is ahead of Frankie. This includes the 3 arrangements you made in step 2.

In Step 2 the arrangements are
J F - - - -
- J F - - -
- - J F - -
- - - J F -
- - - - J F . You have missed some of the arrangements. 5 * 4! = 120.

But the Question says Joey and Frankie are not necessarily together.

Thanks
Raama