Re: GMAT Combinatorics 4

gauravsoni wrote:

Bunuel wrote:

MBAhereIcome wrote:

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

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

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.

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

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

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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