There are 20 bikes in spinning class, the bikes are arranged 4 rows, with 5 bikes in each row. They hope to be in the same row, but cannot request specific bike. Determine the probability that all 5 friends will be in same row with Jeff and dariya at either end.

Question

There are 20 bikes in spinning class, the bikes are arranged 4 rows, with 5 bikes in each row. They hope to be in the same row, but cannot request specific bike.  Determine the probability that all 5 friends will be in same row with Jeff and dariya at either end.

Reiny · Answer

At the ends it could be Jeff, Dariya or Dariya, Jeff
So for the first row:
2x3x2x1 or 12 ways, leaving 15! for the other positions.
but there are 4 rows,
prob(of your event) = 4x12(15!)/20! = .000025799