six children stand outside their classroom they enter classroom and sot in a circular table .in how many ways can they sit such that no two children who were standing next to each other outside are sitting next to each other at the table
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total number of students=6
number of students that can sit with each other=2
total groups =total number of students/number of students that can sit with each other
total groups=6/2=3
6 boys will form 3 groups of two students each
that's why we will take factorial of 2 thrice
=6!/2!2!2!
=6*5*4*3*2*1/2*1*2*1*2*1
hence
=720/8=90 answer
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