A group N > 3 friends are in a room. To decide on a choice of one of three proposals, they decide to proceed following certain rules defined as follows: Each friend writes their name on a slip of paper and drops the slip into a box. The box is well mixed, and one at a time each of the friends draws a slip of paper. The process is terminated if one either one of three things happens: (i) One of the friends get their own name (in which case they chooseproposal 1); (ii) two consecutive friends draw each other's names (that is the person who drew in the ith position draws the name of the person who drew in the i + 1íst position, and the person who drew in the i + 1íst positiondrew the name of the person who drew before (in which case they choose proposal 2); (iii) All the slips of paperare taken (in which case they choose proposal 3). What is the probability that this process stops after the second person draws a slip of paper?
A group N > 3 friends are in a room. To decide on a choice of one of three proposals, they decide to proceed following certain rules defined as follows: Each friend writes their name on a slip of paper and drops the slip into a box. The box is well mixed, and one at a time each of the friends draws a slip of paper. The process is terminated if one either one of three things happens:
(i) One of the friends get their own name (in which case they choose
proposal 1);
(ii) two consecutive friends draw each other's names (that is the person who drew in the ith position draws the name of the person who drew in the i + 1íst position, and the person who drew in the i + 1íst position
drew the name of the person who drew before (in which case they choose proposal 2);
(iii) All the slips of paper
are taken (in which case they choose proposal 3).
What is the
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