Mrs. F has invited several wives of delegates to the United
Nations for an informal luncheon. She plans to seat her 9
guests ina row such that each lady will be able to converse
with the person directly to her left and right. She has
prepared the following list.

Mrs. F speaks English only.

Mrs. G speaks English and French.

Mrs. H speaks English and Russian.

Mrs. J speaks Russian only.

Mrs. K speaks English only.

Mrs. L speaks French only.

Mrs. M speaks French and German.

Mrs. N speaks English and German.

Mrs. O speaks English only.

How many distinct seating arrangements are possible? Give
all possible seating arrangements.

Note that ABCD and DCBA are the same.






Mrs. F has invited several wives of delegates to the United Nations for an informal luncheon. She p..

Answer / guest

126 distinct seating arrangements are possible.

Mrs. J and Mrs. H must be together and Mrs. J must be at the
end as Mrs. J speaks only Russian and Mrs. H is the only
other Russian speaker.

Mrs. L speaks only French and there are two others - Mrs. G
and Mrs. M - who speak French. Here there are 2 cases.

? CASE A : Mrs. L is at the other end

If Mrs. L is at the other end, either Mrs. G or Mrs. M must
seat next to her.

o CASE AA : Mrs. G seats next to Mrs. L

Then, Mrs. M must seat next to Mrs. G and Mrs. N must seat
next to Mrs. M. This is because Mrs. M speaks French and
German, and Mrs. N is the only other German speaker. Thus,
the possible seating arrangement is JHxxxNMGL, where x is
the English speakers. Mrs. F, Mrs. K and Mrs. O can be
arranged in remaining 3 positions in 3! different ways i.e.
6 ways.

o CASE AB : Mrs. M seats next to Mrs. L

If so, then either Mrs. N or Mrs. G must seat next to Mrs. M

? CASE ABA : Mrs. N seats next to Mrs. M

Thus, the possible seating arrangement is JHxxxxNML, where x
is the English speakers. Mrs. F, Mrs. G, Mrs. K and Mrs. O
can be arranged in remaining 4 positions in 4! different
ways i.e. 24 ways.

? CASE ABB : Mrs. G seats next to Mrs. M

Thus, the possible seating arrangement is JHxxxxGML, where x
is the English speakers. Mrs. F, Mrs. K, Mrs. N and Mrs. O
can be arranged in remaining 4 positions in 4! different
ways i.e. 24 ways.

? CASE B : Mrs. L does not seat at the end

It means that Mrs. G, Mrs. L and Mrs. M must seat together.
Also, Mrs. L must seat between Mrs. G and Mrs. M.

o CASE BA : Mrs. G seats left and Mrs. M seats right to Mrs.
L i.e. GLM

? CASE BAA : GLM is at the other end

Thus, the possible seating arrangement is JHxxxxGLM, where x
is the English speakers. Mrs. F, Mrs. K, Mrs. N and Mrs. O
can be arranged in remaining 4 positions in 4! different
ways i.e. 24 ways.

? CASE BAB : GLM is not at the other end

Then Mrs. N must seat next to Mrs. M. Now, we have a group
of four GLMN where Mrs. G and Mrs. N speak English. Thus,
the possible seating arrangement is JHxxxX, where x is the
individual English speakers and X is the group of four
females with English speakers at the both ends. Thus, there
are 4! different ways i.e. 24 ways.

o CASE BB : Mrs. M seats left and Mrs. G seats right to Mrs.
L i.e. MLG

Then, Mrs. N must seat next to Mrs. M. Now, we have a group
of four NMLG where Mrs. G and Mrs. N speak English. Thus,
the possible seating arrangement is JHxxxX, where x is the
individual English speakers and X is the group of four
females with English speakers at the both ends. Thus, there
are 4! different ways i.e. 24 ways.

Thus, total different possible seating arrangements are :

= 6 (case AA) + 24 (case ABA) + 24 (case ABB) + 24 (case
BAA) + 24 (case BAB) + 24 (case BB)

= 126 seating arrangements

Thus, 126 distinct seating arrangements are poosible.

Is This Answer Correct ?    0 Yes 0 No

Post New Answer




More Puzzles Interview Questions

day before yesterday i was 25 years , next year iam 28,when is my birthday? which day is today?

8 Answers  


4 men can dig 4 holes in 4 days. How many hours does it take for 1 man to dig half a hole?

8 Answers  


Why do you want to do job in Pharma midical company?

1 Answers  


A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion. First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop. Finally how far he is from his camp and in which direction?

1 Answers  


if u love someone u can arrange these 10 letters in 5 words I H O M U R E Y N A

41 Answers   Infosys, DQ Entertainment, Era Infra Engineering,






There are N secret agents each know a different piece of secret information. They can telephone each other and exchange all the information they know. After the telephone call, they both know anything that either of them knew before the call. What are the minimum number of telephone calls needed so that all of the them know everything?

8 Answers   Microsoft,


A man was looking at a portrait. Someone asked him, "Whose picture are you looking at?" He replied, pointing at the portrait: "Brothers and sisters have I none, but this man's son is my father's son." Now whose picture is the man looking at?

6 Answers   University,


What is the area of the triangle ABC with A(e,p) B(2e,3p) and C(3e,5p)? where p = PI (3.141592654)

2 Answers  


A man got 30 aples in 1 Rs.Now he want 20% of profit on it. How many apples He should Sell in 1 Rs.??

20 Answers   TCS,


A person travels on a cycle from home to church on a straight road with wind against him. He took 4 hours to reach there. On the way back to the home, he took 3 hours to reach as wind was in the same direction. If there is no wind, how much time does he take to travel from home to church?

3 Answers  


In the General meeting of "Friends Club", Sameer said, "The repairs to the Club will come to a total of Rs 3120 and I propose that this amount should be met by the members, each paying an equal amount." The proposal was immediately agreed. However, four members of the Club chose to resign, leaving the remaining members to pay an extra Rs 26 each. How many members did the Club originally have?

3 Answers  


3. During a recent school reunion, four men were discussing their starting salaries back in 1962. the salaries in questring were 8, 10,12 and 14 thousand pounds per year. of course the MP earned the most. Alan earned more than Brian and the doctor earned more thanb Derek, the vet. carles could not remember what he started on. Brian, the lawyer, did not start on 10,000 pounds nor did Derek. can you determine who has which job and their starting salaries?

2 Answers  






Categories