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________.

Including the two specified people, 4 others can be selected ,${ }^5{\mathrm{C}}_4$ways. The two adjacent seats can be taken in 4 ways and the two
specified people can be arranged in 2! ways, remaining 4 people can be arranged in 2! ways. Therefore, $5{\mathrm{C}}_4\cdot 4\cdot 2!4!=5!8=8\cdot 5!$