Question 33

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 batchmates 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 batchmates are not sitting next to each other, is:

Solution

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Consider the case where batchmates are sitting together and then subtract those cases from total no. of cases.

When 10 students are arranged in a line, total arrangements possible are 10!

Now considering batchmates sitting together, 

B1 B2  _ _ _ _ _ _ _ _

Then total arrangements possible are 9!*2!

Total ways = 10! - 9!*2!

9!*8 =  2903040

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