A total of 6 Boys and 6 girls are to sit in a row alternatively and in a circle. Let m be the number of arrangements in the row and n be the number of arrangements in the circle. If k = m 10 n , then the value of k is

Step-by-step solution

Linear permutations with boy in the first place are of the form B 1 G 1 B 2 G 2 B 3 G 3 B 4 G 4 B 5 G 5 B 6 G 6 and the number of such arrangements is 6 ! × 6 ! . The number of linear permutations with girl in the first place is 6 ! × 6 ! So, the number of arrangements in row = m = 2 × 6 ! × 6 ! (In circular permutations, start with a place which can be filled by a boy or a girl and after that the arrangements become linear) Placing the boys first and then arranging the girls in 6 gaps, the number of such circular