There are fifty persons among whom 2 are brothers. The number of ways they can be arranged in a circle, if there is exactly one person between the two brothers, is

Step-by-step solution

Consider three persons as one unit. This unit and remaining 47 persons (total 48 ) can be arranged in a circle in 47 !   ways. In this unit, the two brothers can be interchanged in 2 ways. The person between the two brothers can be any of the remaining 48 persons who can be selected in C   48 1 ways. Hence, the required number of ways = C   48 1 × 47 ! × 2 = 2 × 48 !