Juan and his five friends will sit on six fixed seats around

Question

Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?

(A) 20
(B) 24
(C) 48
(D) 72
(E) 120

(A) 20
(B) 24
(C) 48
(D) 72
(E) 120

Bunuel · Accepted Answer

2*3! = 12 not 48, also there are total of 6 people so without Juan and Jamal there are 4 left not 3.

As the Juan's seat is fixed and Jamal must sit next to him then they can be seated only in 2 ways:  {Juan} {Jamal} or {Jamal} {Juan} . Other 4 friends can be seated in 4! ways, so total 2*4!=48.

Bunuel · Answer

Since Juan's seat is fixed, then circular arrangement is not applicable here. You see, since Juan's seat is fixed, the number of arrangements of four friends (except Jamal) is 4! irrespective whether they are in front of Juan or in circle with him.

Hope it's clear.

yangsta8 · Answer

J = Juan, F = Jamal
Since J is always fixed, set J, set F relative to J, then see how many options there are:
J F 4 3 2 1 = 24 or
F J 4 3 2 1 = 24

24+24=48 … C

MBAhereIcome · Answer

count juan and jamal as one member that sits on a fixed chair. now we are left with 3 more members who can sit in 3! ways.
jamal can sit on either side of juan so total combinations = 2*3! = 48

ans: c

Stiv · Answer

Isn't the result 24?! Juan must sit on the seat closest to the window and cannot swap his seat with Jamal because if they swap seats Juan won't be closest to the window (which is a must). The others can sit in 4! ways.

Bunuel · Answer

Juan's seat is fixed, yes. But Jamal can be to the right of him or to the left.

jlgdr · Answer

What about the fact that the table is circular? Don't we need to use the formula (n-1)! say instead of 4! we would have 3!? Thanks Cheers! J

calmkeeper · Answer

answering the question about (n-1)! formula

consider Juan and Jamal as one unit (as they always sit at adjacent places), as if we had 5 people altogether. using the formula for circular arrangement (n-1)! we have (5-1)!, and then multiplying the result be 2! to take into account arrangements inside our unit Juan+Jamal

gauravsoni · Answer

Hi Bunuel, could you please explain why do we multiply by 2 in the following 2*4! (its 4! because we are considering Juan and jamal as 1 so thats fine). Really bad with combinations and probability

Bunuel · Answer

Those two cane be arranged either {Juan} {Jamal} or {Jamal} {Juan} . For each of these arrangements the remaining 4 can be seated in 4!, so total is 2*4!. Does this make sense? Theory on Combinations: math-combinatorics-87345.html DS questions on Combinations: search.php?search_id=tag&tag_id=31 PS questions on Combinations: search.php?search_id=tag&tag_id=52 Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html Theory on probability problems: math-probability-87244.html All DS probability problems to practice: search.php?search_id=tag&tag_id=33 All PS probability problems to practice: search.php?search_id=tag&tag_id=54

gauravsoni · Answer

Those two cane be arranged either {Juan} {Jamal} or {Jamal} {Juan} . For each of these arrangements the remaining 4 can be seated in 4!, so total is 2*4!. Does this make sense? Theory on Combinations: math-combinatorics-87345.html DS questions on Combinations: search.php?search_id=tag&tag_id=31 PS questions on Combinations: search.php?search_id=tag&tag_id=52 Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html Theory on probability problems: math-probability-87244.html All DS probability problems to practice: search.php?search_id=tag&tag_id=33 All PS probability problems to practice: search.php?search_id=tag&tag_id=54 Thanks Bunuel , been doing combinations and probability since morning. Finally getting a hang of it

. Thanks for the links

MK1480 · Answer

Using FCP rule

seat1 -  1 way  - John can sit at any place in 1 way
Seat2 -  2 ways  - Jamal should sit next to him. either left or right
seat 3 -  4 ways  - 4 people remaining. anyone can sit anywhere
Seat 4 -  3 ways  - 3 people can sit anywhere
Seat 5 -  2 ways  - 2 people can sit anywhere
Finally, 
Seat6 -  1 way  - 1 person & 1 seat available

Total = 1 x 1 x 4 x 3 x 2 x 1 = 48 ways

HolaMaven · Answer

What do u mean by closest to circle than? There is going to be only one seat closest to window then why 48?

ScottTargetTestPrep · Answer

Since Juan and Jamal must sit next to each other in a specific location (next to the window), they can be arranged in 2! ways (Juan-Jamal or Jamal-Juan).

Then we need to arrange the 4 remaining friends, who can be arranged in 4! = 24 ways. Thus, the total number of ways to arrange the group is 2 x 24 = 48.

Answer: C

HolaMaven · Answer

But if window is close to first seat than arrangement for Jamal and Juan is going to be Juan(seat closest to windoe)- Jamal (next seat).

ShankSouljaBoi · Answer

A-- Juan has only way to seat. This does the identification of the seats on the table.

B-- Now, jamal has two places to sit

C-- the remaining can permute among 4 vacant seats on the table in 4! ways

Final Answer = A*B*C = 1*2*24 = 48

C it is

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CEdward · Answer

F is Juan's friend.

Case 1: 
JF

Case 2: 
FJ

Consider them a unit so there's really only 5 people

(5-1)! = (4)! = 4! = 24

24 x 2 = 48

Answer is C. Note that the window is inconsequential and is just there to distract you.

pierjoejoe · Answer

IMO the solution is considering 2 seats already occupied (one near the window, the other by Jamal, that seats next to Juan). the other friends can seat in 4! ways. but we also have to take into account that Jamal can be either seated on the right or left of Juan. both of the option have 4! possible ways of arranging the other 4 friends (as explained before), thus--> 2*4! = 2*24 = 48

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Juan and his five friends will sit on six fixed seats around

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