During the essay writing stage of MBA admission process in a reputed B-School

During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batch mates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batch mates are not sitting next to each other, is

  1. 3540340
  2. 2874590
  3. 2903040
  4. None of the above

Solution

Number of ways in which 10 students can sit = 10!

Considering batch mates as single unit, number of ways in which batch mates sit together = 9! × 2

The number of ways in which the student can sit so that the two batch mates are not sitting next to each other = 10! - (9! × 2)

= 9! × 8 = 2903040

The correct option is C.