Question
The number of ways can 7 boys be seated at a round table so that 2 particular boys are separated is :



 6!2!
Hint:
Total number of ways in which they are separated = Total ways of arranging 7 boys at a round table  Total ways of arranging 2 boys sitting together
The correct answer is:
Step by step solution :
We want to find the numbers of ways in which 7 boys can be seated on a round table when 2 particular boys are seperated.
Let us assume that two boys put together a single unit.
Now, we will arrange 6 entities in 6 places on a circular table.
When n objects are arranged in n places in a circular table, then there are (n−1)! ways.
That is, if there are 6 boys and 6 places, then there are (6−1)! ways to arrange.
Now, the two boys that were fixed in a single place can also rearrange themselves.
The number of ways in which two boys can arrange among themselves is 2!
Next, to find the number of ways 7 boys can be seated at a round table so that 2 particular boys are next to each other is multiply 5! with 2!
That is, total ways possible are 5!2!.
Total ways of arranging 2 boys sitting together = 5! 2! = 240.
Total ways of arranging 7 boys at a round table = (7–1)! = 6! = 720
Total number of ways in which they are separated = Total ways of arranging 7 boys at a round table  Total ways of arranging 2 boys sitting together
Thus, Total number of ways in which they are separated = 720  240 = 480
When n distinct objects are arranged in n places, then the total number of ways possible are n!. But, when n objects are to arranged in n places on a circular table, there are (n−1)!ways.
Related Questions to study
Least ionic compound among the following is
Least ionic compound among the following is
Stability of ionic compound is influenced by
Stability of ionic compound is influenced by
The electronegativities of F,Cl,Br and I are 4.0,3.0,2.8,2.5 respectively. The hydrogen halide with a high percentage of ionic character is
The electronegativities of F,Cl,Br and I are 4.0,3.0,2.8,2.5 respectively. The hydrogen halide with a high percentage of ionic character is
The eccentricity of the hyperbola with asymptotes 3x + 4y = 2 and 4x – 3y = 2 is
The eccentricity of the hyperbola with asymptotes 3x + 4y = 2 and 4x – 3y = 2 is
The number of ways that '6' rings can be worn on the 4  fingers of one hand is
It is important to note that we have used a basic fundamental principle of counting to find the total ways. Also, it is important to notice that each ring has 4 ways as it has not been given that each finger must have at least one ring. So, there can be 6 rings in a finger alone and remaining all the fingers empty.
The number of ways that '6' rings can be worn on the 4  fingers of one hand is
It is important to note that we have used a basic fundamental principle of counting to find the total ways. Also, it is important to notice that each ring has 4 ways as it has not been given that each finger must have at least one ring. So, there can be 6 rings in a finger alone and remaining all the fingers empty.