A basic stadium has 48 seats arranged in 8 rows by 6 seats e

A basic stadium has 48 seats arranged in 8 rows by 6 seats each. 3 fans buy tickets for the same concert idependently of each other. Determine the probability that they will be seated in the same row. Please show all work and explanations so I can apply it to future problems. Thanks

Solution

number of ways 3 people can be seated in 48 seats = ⁴⁸P₃ = 48*47*46

number of ways 3 people can be seated in 6 seats (one row = 6 seats) = ⁶P₃ = 6*5*4

number of ways 3 people can sit in same row out of 8 rows each having 6 seats = 8 * ⁶P₃ = 8 * 6*5*4

probebility that 3 people will sit in same row = 8*6*5*4 / (48*47*46) = 10 / 1081