A and B stand in a circular ring with 10 other persons. If the arrangement of 12 persons is randomly done, the chance, that there are exactly 3 persons between A and B is A and B stand in a circular ring with 10 other persons. If the arrangement of 12 persons is randomly done, the chance, that there are exactly 3 persons between A and B is

There are total 12 persons A + B + 10 others. So, total number of ways to be arranged around a circle = (12-1)!= 11! Ways Now, exactly 3 persons are to be arranged in between A and B. So, ¹⁰P3 Now, A and B can interchange their positions = 2! Ways Also, the remaining 7 can also interchange their positions with each other. So, 7! Ways So, total ways in arranging all with the condition of exactly 3 in between A and B = 2!* ¹⁰P3* 7! Ways =2*(10!/7!) *7!= 2*10! Ways So, the chance (Probability) = 2*10!/11! = 2/11