Erik and Joe..

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mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Sat Sep 10, 2011 12:54 am

Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?

it is easy Q but i am a bit confused when i am going to solve easier Qs based on more challenging Qs i tried to underestand in probability and combination... to me the approach is 3!/2! = 3 ways
while the answer is 4 ways...

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Source: Beat The GMAT — Problem Solving | Sat Sep 10, 2011 12:54 am

mehrasa: Master | Next Rank: 500 Posts; Posts: 279; Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member; Thanked: 15 times

by mehrasa » Sat Sep 10, 2011 12:58 am

when i want to solve it without formula i can figure out where this four come
let,s say the third name is kevin.. different arrangement are as follows:
JEK
EJK
KEJ
KJE

could u plz tell me how I can find it with formula?

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sat Sep 10, 2011 1:03 am

let persons by k,e,j.
e and j sit together, so put them in a box.
Now we have 'k' and a box. no. of ways to arrange them = 2!
Now in between box, we can arrange e,j in 2 ways: (ej,je)
thus 21*2 = 4 ways

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Sep 10, 2011 2:50 am

mehrasa wrote:Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?

it is easy Q but i am a bit confused when i am going to solve easier Qs based on more challenging Qs i tried to underestand in probability and combination... to me the approach is 3!/2! = 3 ways
while the answer is 4 ways...

Let the 3 people be E, J , and K.
Now since E must sit next to J, so treat them as 1 person.
So, the possible arrangements are 2!
Now, E and J can also interchange places among themselves, which can be done in 2 ways (EJ and JE)

So, the possible no. of sitting arrangements are 2! * 2 = 4 ways

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rohit56: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Sat Dec 15, 2018 12:06 am

by rohit56 » Mon Dec 17, 2018 10:17 pm

Consider Eric and joe as one person. Then we have total 2 persons to be seated.
No of ways of doing so = 2 ways
Now, Eric and joe could also be arranged in 2 different ways i.e Erik left to Joe and Erik right to Joe.
Hence, total ways = 2 x 2 = 4

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