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At the Buck family reunion, five sets of twins from five different generations decide to have a bike race, with two teams and one sibling from each set of twins on each team. Each team sets off with all five cyclists in a line behind their “captain”. At any point in the race, the last person in the line can cycle to the front of the line to become the new captain. All five team members must cross the finish line to complete the race.
Both teams line up in age order but Team A starts the race with a little kid as their captain and Team B starts the race with an elderly woman as their captain. During the course of the race, the captains change six times between the two teams. When the teams cross the finish line, what are the odds that their captains will be the same age?