Analytical - Six people A,B,C,D,E and F went to cinema and want to sit as A is followed by B ,followed by c, foll

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Six people A,B,C,D,E and F went to cinema and want to sit as A is followed by B ,followed by c, followed by D ,followed by E, followed by F.
    B wants to sit on any side of A.
    C wants to sit by the side of A or B.
    D wants to sit by the side of A or B or C
    E wants to sit by the side of A or B or C or D.
    F wants to sit by the side of A or B or C or D or E.
now the question is how many combinations are possible to sit as mentioned above.

Total Answers and Comments: 10

Last Update: May 25, 2008

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Best Rated Answer

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Submitted by: dinesh

ans is 240

for a, b , c there are only 4 combinations since c cant come in b/w like wise d has 12 combinations

abcd acbd bacd cabd bcad cbad

dabc dacb dbac dcab dbca dcba ,

hence we can derive a simple eqn i.e for a, b,c=2! *2 =4

for a,b,c,d = 3! *2 =12

fora,b,c,d, e = 4! * 2 = 48

for a,b,c,d,e,f = 5!*2 =240

Above answer was rated as good by the following members:
Mohammed Aijaz Ahmed

July 06, 2005 19:45:26

Raghu

RE: Six people A,B,C,D,E and F went to cinema and want to sit as A is followed by B ,followed by c, foll...

For ex consider for A B the combos are A B and B A i.e 2 combos are possible.

For ex consider for A B C the combos (C A B) (A C B) (B A C) and (C B A) i.e 4 combos are
possible.

llly for A B C D the combos wld get doubled i.e 8

for A B C D E the combos wld get doubled i.e 16

for A B C D E F the combos wld get doubled i.e 32

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0 1

Overall Rating: -1

September 28, 2005 07:15:20

nagu

RE: Six people A,B,C,D,E and F went to cinema and want...

correct

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November 25, 2005 14:09:31

Nishant Joshi

RE: Six people A,B,C,D,E and F went to cinema and want...

the above sol is right but one combination is wrong ...

c cant come in middle of a and b so it shud be

(cab)(abc)(cba)(bac)

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January 31, 2006 04:14:36

praveena

RE: Six people A,B,C,D,E and F went to cinema and want...

if we take second combination a b c. we can get 6 combinations i.e. (a b c) (a c b) (b a c) (b c a) (c b a) (c a b).

check it

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February 23, 2006 14:24:48

sarfaraj

RE: Six people A,B,C,D,E and F went to cinema and want...

In case of a b cc cant come in betn a & b as mention -side of a or b hence only 4 possible cases

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October 16, 2006 09:01:10

dinesh

RE: Six people A,B,C,D,E and F went to cinema and want...

ans is 240

for a b c there are only 4 combinations since c cant come in b/w like wise d has 12 combinations

abcd acbd bacd cabd bcad cbad

dabc dacb dbac dcab dbca dcba

hence we can derive a simple eqn i.e for a b c 2! *2 4

for a b c d 3! *2 12

fora b c d e 4! * 2 48

for a b c d e f 5!*2 240

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October 29, 2006 03:44:17

indu

RE: Six people A,B,C,D,E and F went to cinema and want...

there cant be six combinations with a b c coz c cant sit in between a and b

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January 02, 2007 02:04:22

sandeep

RE: Six people A,B,C,D,E and F went to cinema and want...

@ dinesh hey just want to correct you on ur answer of 12.... one of the condition mentioned is b wants to sit on any side of A and c takes seat after b so you cant have combinations that include acb where c comes in between a n b ... so there are just 8 arrangements and not 12 ... over all there are 32 such combinations.

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February 16, 2008 07:52:18

chozha

Member Since: February 2008 Contribution: 5

RE: Six people A,B,C,D,E and F went to cinema and want to sit as A is followed by B ,followed by c, followed by D ,followed by E, followed by F. B wants to sit on any side of A. C wants to sit by the side of A or B

it is clear that "c" cannot come in between a and b.so 4 combinations is right.

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May 25, 2008 23:34:16

#10

pavan04kumar

Member Since: May 2008 Contribution: 1

hiiiiiii

first B should be in the side of A so let us fix them as AB i.e they can be arranged 2! 2

C shold be in the side of A or B ie (AB)C or C(AB) 2! and A and B can be arranged among them in 2! ways from above i.e total it can be arranged 2! * 2! 4

now for D ABC are fixed as (ABC)D or D(ABC) so it can be arranged in 4* 2! 8

similarly for E 8* 2! 16

simlarly for F 16* 2! 32

so total no. of combinations after F is placed is 32 .... i suppose 32 as answer .... i am not sure abt my answer .... please correct me if i am wrong ....

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