Answer
305.4k+ views
Hint: The most important formula when it comes to circular permutation is that:
When there are $n$ people, they have to be arranged around a circular table, the total number of ways of arranging them are: $\dfrac{{n!}}{n} = (n - 1)!$
Complete step-by-step answer:
We have to arrange 6 gentlemen and 3 ladies such that every gentleman has a lady by his side.
We can start by first arranging the men around the table.
The number of ways it can be done is: $(6 - 1)! = 5! = 120$
Now, we can place the three ladies in such a way that every man has a lady on either of his side.
The number of ways of arranging the ladies is: $3! = 6$
The number of ways of arranging both men and ladies is: $120 \times 6 = 720$
Since, their left and right sides can be interchanged but still the given condition will be obeyed, the total number of ways the given arrangement can be done is:
(Number of ways of arranging men) $ \times $ (number of ways of arranging women)
$720 \times 2 = 1440$
So, the correct answer is “Option A”.
Note: When the things or people are arranged around a circle, then it’s called circular permutation. We have to remember the formula of circular permutation which is: $\dfrac{{n!}}{n} = (n - 1)!$ .
If the clockwise and anti-clockwise can be distinguished, for example when it involves people, we have to multiply it with 2.
If the clockwise and anti-clockwise can not be distinguished, for example when it involves flowers, multiplication with 2 is not required.
When there are $n$ people, they have to be arranged around a circular table, the total number of ways of arranging them are: $\dfrac{{n!}}{n} = (n - 1)!$
Complete step-by-step answer:
We have to arrange 6 gentlemen and 3 ladies such that every gentleman has a lady by his side.
We can start by first arranging the men around the table.
The number of ways it can be done is: $(6 - 1)! = 5! = 120$
Now, we can place the three ladies in such a way that every man has a lady on either of his side.
The number of ways of arranging the ladies is: $3! = 6$
The number of ways of arranging both men and ladies is: $120 \times 6 = 720$
Since, their left and right sides can be interchanged but still the given condition will be obeyed, the total number of ways the given arrangement can be done is:
(Number of ways of arranging men) $ \times $ (number of ways of arranging women)
$720 \times 2 = 1440$
So, the correct answer is “Option A”.
Note: When the things or people are arranged around a circle, then it’s called circular permutation. We have to remember the formula of circular permutation which is: $\dfrac{{n!}}{n} = (n - 1)!$ .
If the clockwise and anti-clockwise can be distinguished, for example when it involves people, we have to multiply it with 2.
If the clockwise and anti-clockwise can not be distinguished, for example when it involves flowers, multiplication with 2 is not required.
Recently Updated Pages
The deliquescent among the following is ACaCl2 BFeSO47H2O class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The d electron configurations of Cr2 + Mn2 + Fe2 + class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of ionization of a 01M bromoacetic acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of Hydrolysis of CH3COONH4 is independent class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name 10 Living and Non living things class 9 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
List some examples of Rabi and Kharif crops class 8 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)