The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together is

Step-by-step solution

Given, 7 boys and 5 girls are to be seated around a circular such that no two girls to be seated together, Now we know that n objects can be arranged in a circle in ( n - 1 ) ! ways. Let us first arrange 7 boys in circular arrangement in 7 - 1 ! ways. Now there will be 7 gaps. So let us select any 5 gaps out of 7 gaps and arrange 5 girls in the chosen gaps. This can be done in C 5 7 × 5 ! ways. Hence, required arrangements are 6 ! × C 5 7 × 5 ! = 6 × 5 ! × 7 × 6 2 × 5 ! = 126 5 !