page 3 . MATH 2030 - Final Exam 2 . 10 participants in a race are identified as runners a , b . .... ] . The lanes for the race are labelled 1 , 2 , ... . 10 with lanes 1 and 10 being " outside" lanes , and the rest being* " inside " lanes . A race lineup is determined by assigning each runner to a lane , with exactly one runner in each lane . ( 2 ) 15 ) How many race lineups are possible ? ( b) |5] How many possible lineups have at least one of the outside lanes occupied by runners a , 6 , or C ? ( c ) 15 ] A race lineup is chosen at random , with all lineups being equally likely . Suppose that all 10 runner are of comparable speed , but that runners a and 6 work as a team whenever they are in neighbouring lanes . This means that if a and b are in lanes next to each other , a will win the race ; of the time . While if they are not in lanes next to each other , a will only win to of the time . Given that a wins the race , what is the conditional probability that 6 ran in a neighbouring lane