Interested to Buy Any Domain ? << Click Here >> for more details...
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.
- 1 Answers
- 5323 Views
- I also Faced
- E-Mail Answers
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 |
Three containers are of 15,10 and 6 ltrs capacity. Initially its in configuration (15,0,0). Make it to configuration (2,8,5).
Given two bucket of large capacity. There are 100 black ball and 100 white ball. Distribute the balls among two bucket such that probability of choosing a white ball is maximum.
How long would it take you to count 1 billion orally if you could count 200 every minute and were given a day off every four years?
wat will be the next number in the series.... 1,3,5,9,12,21,..
9 9 9 9 5 5 5 5 3 3 3 3 1 1 1 1 is me se kin 6 number ka total 21 hota he..? its challange..
53 Answers Bhel, TCS, TGB,
|3\3 9/9| ! 3["9"" ["39"" | \9/ | ¡ "9""]3 ""9"] YOU "" "" understand this Mssg!! Send
5 Answers Olive Builders, Satyam,
At the Party: 1. There were 9 men and children. 2. There were 2 more women than children. 3. The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible. Also, of the three groups - men, women and children - at the party: 4. There were 4 of one group. 5. There were 6 of one group. 6. There were 8 of one group. Exactly one of the above 6 statements is false. Can you tell which one is false? Also, how many men, women and children are there at the party?
Taurus+pisces =scorpio,substitute the digits for the following letter to make the following addition true?
A boy found that he had a 48 inch strip of paper. He could cut an inch off every second. How long would it take for him to cut 48 pieces? He can not fold the strip and also, can not stack two or more strips and cut them together.
Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.
16 Answers Directi, Infosys, L&T, Shreyas, TCS, Turing Software,
Makayla had $1.19 in change. None of the coins was a dollar. Nicole ask her for change for a dollar, but Makayla could not make change. What coins did she have?
we have 3 rows 3 columns there in 1st row and 2nd column we have 8 values, so we add from any row or column we get value 15 please tell me how to find out this value
English 
