Question

How many ways can john sit to the left of tom but not necessarily beside him in a row of 7 people

Answer 1

Tom and John are to sit in a row of 6 seats with 4 other people. Number of ways for 6 people to sit if Tom sits to the left of John (but not necessarily directly beside him) is given by N = John on extreme right seat (#6) P(5, 1)*P(4, 4) + John on seat #5 P(4, 1)*P(4, 4) + John on seat #4 P(3, 1)*P(4, 4) + John on seat #3 P(2, 1)*P(4, 4) + John on seat #2 P(1, 1)*P(4, 4) = P(4, 4)[5 + 4 + 3 + 2 + 1] = 24*15 = 360 ANSWER P(4, 4) is the number of ways seating 4 others on remaining 4 seats when John has seated and Tom has seated on his left in P(5, 1), P(4, 1), P(3, 1), P(2, 1), P(1,1) ways.