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# Combinatorics

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Intern
Joined: 13 May 2009
Posts: 18
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Kudos [?]: 15 [0], given: 1

Combinatorics [#permalink]  04 Aug 2009, 12:38
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:28) correct 0% (00:00) wrong based on 0 sessions
Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to other dwarf and no elf will sit to another elf, in how many different ways can the elves and dwarves sit?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2140 [0], given: 359

Re: Combinatorics [#permalink]  04 Aug 2009, 12:46
Expert's post
1) There is 2 possible options how dwarves and elves could be placed: dedede or ededed

2) There is $$P_3^3$$ options for 3 dwarves/elves for choosing 3 chairs

3) Finally, $$2*P_3^3*P_3^3 = 2*3!*3! = 72$$
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Intern
Joined: 13 May 2009
Posts: 18
Followers: 0

Kudos [?]: 15 [0], given: 1

Re: Combinatorics [#permalink]  04 Aug 2009, 13:00
Two Options :-

1.) DEDEDE

2.) EDEDED

Persons Choices Seat Assigned

Dwarf A 6 Choices(1,2,3,4,5,6) #1
Dwarf B 2 Choices(3,5) #3
Dwarf C 1 Choice(5) #5
ELF A 3 Choices(2,4,6) #2
ELF B 2 Choices(4,6) #4
ELF C 1 Choice(6) #6

Final product 6*2*1*3*2*1 =72

If the same process is followed for option 2 we will get the same result of 72. In that case the answer should be 72+72?? Correct me if i am wrong!
Senior Manager
Joined: 17 Jul 2009
Posts: 299
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Followers: 1

Kudos [?]: 35 [0], given: 9

Re: Combinatorics [#permalink]  04 Aug 2009, 14:01
lbsgmat wrote:
Two Options :-

1.) DEDEDE

2.) EDEDED

Persons Choices Seat Assigned

Dwarf A 6 Choices(1,2,3,4,5,6) #1
Dwarf B 2 Choices(3,5) #3
Dwarf C 1 Choice(5) #5
ELF A 3 Choices(2,4,6) #2
ELF B 2 Choices(4,6) #4
ELF C 1 Choice(6) #6

Final product 6*2*1*3*2*1 =72

If the same process is followed for option 2 we will get the same result of 72. In that case the answer should be 72+72?? Correct me if i am wrong!

because your Dwarf A could choose among all 6 seats, so that's including both option 1 and 2 there
Manager
Joined: 18 Jul 2009
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Location: India
Schools: South Asian B-schools
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Kudos [?]: 64 [0], given: 37

Re: Combinatorics [#permalink]  06 Aug 2009, 08:41
dedede or ededed

Hence 3! x 3! x 2 = 72
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Re: Combinatorics   [#permalink] 06 Aug 2009, 08:41
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