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Question

Seven persons draw lots for the occupancy of the six seats in a first class railway compartments: find the chance (1) that two specified persons obtain opposite seats, (2) that they obtain adjacent seats on the same side.

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Solution

Let the two persons be A and B
Probability of getting a seat for let say A =67
Now there is only one seat opposite to A
Now probablility that B is oppsoite to A =67×16=17
Any two adjacent seats can be selected in 7C2=21 ways
Now A and B can be seated adjacent in 4 ways
required probability =421


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