I\'ve made this problem from real-life experience and found it challenging.\n\nTwo people get prepared for performance. They required to attend **all four** rehearsal stages. Performance organizers made timetable convenient for all people by making every stage **repeated seven** times, and anyone can freely choose a date.\n\nA person can take any order of rehearsals, but the first stage must be taken first.\n\n**Calculate probability for these two persons to meet at rehearsals, if they made completely random and independent date choices.**\n\nExample of the timetable (t) and day (d, given for convinience):\n```\nt = [1, 2, 1, 3, 1, 2, 3, 4, 1, 3,  2,  4,  2,  1,  4,  1,  3,  1,  4,  2,  3,  4,  2,  4,  3,  4,  2,  3]\nd = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]\n```\n\nThe number means the rehearsal stage.\nExamples of valid sequences: `[0, 1, 3, 7], [4, 5, 6, 7], [8, 9, 11, 12]` \u2014 all stages taken and first is first\nExamples of invalid sequences: \n`[0, 1, 2, 3]` \u2014 stage `4` not taken;\n`[1, 2, 3, 7]` \u2014 stage `2` taken first, should be `1`\n\nAs a bonus show how the probability of meeting declines, depending on the chosen date of the first rehearsal.\n\nAs an additional bonus, show how the ability to choose more than four rehearsals affects the result. \nFor example, a person can take sequence `[0, 1, 3, 5, 7]` if he wants to repeat the stage `2`.

I\'ve made this problem from real-life experience and found it challenging.\n\nTwo people get prepared for performance. They required to attend all four rehears