Question 1194841

use permutation

Thus the number of ways of arranging n persons along a round table so that no person has the same two neighbors is:

total number of boys and girls is {{{6}}}

{{{(n-1)!/2=(6-1)!/2=4!/2=(4*3*2*1)!/2=4*3=12}}}

or, you can do it this way;

condition: each girl is to be between two boys

in group of three there will be {{{2}}} boys and {{{1}}} girl; 

Three boys can be seated first at the round table in {{{2! = 2}}} ways.
Then the three girls can be seated in {{{3}}} gaps in {{{3! = 6}}} ways.
Hence the required number of ways = {{{2* 6 = 12}}} ways