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
joey
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kanha81
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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
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!
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krisraam
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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.kanha81 wrote: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
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!
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