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The number of ways in which six boys and six girls can be seated at a round table so that no two girls sit together and two particular girls do not sit next to a particular boy 15
 

 

Option: 1

6 ! 4 !


Option: 2

2.5 ! 4 !


Option: 3

2.6 ! 4 !

 

 

 


Option: 4

514 !


Answers (1)

best_answer

 The boys can be seated in 5 ! ways.
If the girls g_1 and g_2 do not want to sit by the side of A_1 (say). The two gaps A_6-A_1  and A_1-A_2 must be filled by two of the remaining in { }^4 P_2 ways.
The other four gaps can be filled in 4 ! ways.
Hence the number of ways = 5 ! \times{ }^4 P_2 \times 4 !\\

                                            \begin{aligned} & =5 ! \times \frac{4 !}{2 !} \times 4 ! \\ & =2.6 ! 4 ! \end{aligned}

                                                 

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Pankaj

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