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Q.

Number of ways in which 7 people can occupy 6 seats, 3 seats on each side in a first class railway compartment if two specified persons are to be always included and occupy adjacent seats on the same side is (5!).k, then k has the value equal to________.

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answer is 8.

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Detailed Solution

Including the two specified people, 4 others can be selected , 5C4ways. The two adjacent seats can be taken in 4 ways and the twospecified people can be arranged in 2! ways, remaining 4 people can be arranged in 2! ways. Therefore, 5C4⋅4⋅2!4!=5!8=8⋅5!
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