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  • Find the number of ways to arrange 6 boys and 2 girls around a circular table such that all the girls sit together.Option: 1 1440

Find the number of ways to arrange 6 boys and 2 girls around a circular table such that all the girls sit together.

Option: 1

1440


Option: 2

1230


Option: 3

1730


Option: 4

2320


Answers (1)

To find the number of ways to arrange 6 boys and 2 girls around a circular table such that all the girls sit together, we can treat the group of girls as a single entity. This reduces the problem to arranging 7 entities ( 1 group of girls and 6 boys) around a circular table.


The number of ways to arrange 7 entities around a circular table is,

        (7-1) !=6 !
Within the group of girls, the girls can be arranged among themselves in 2! (2 factorial) ways.

Therefore, the total number of different ways to arrange the 6 boys and 2 girls around a circular table, with all the girls sitting together, is


     6 ! \times 2 !=720 \times 2
     6 ! \times 2 !=1440


Hence, there are 1,440 different ways to arrange the 6 boys and 2 girls around a circular table such that all the girls sit together.

Posted by

Kshitij

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