A team of six students play the following game. They enter a room one by one in any order until all six of them take their turns. In the room, there is a table with a row of six identical boxes labelled 1, 2, 3, 4, 5, 6 that corressponding to the studunt name. Inside each box is the name of one person, randomly chosen so that each person’s name appears in exactly one box. Once inside the room, each person is allowed to open and look inside 5 boxes of their choice. After each person has opened their five boxes they must leave the room, making sure that the boxes are in exactly the same state as before, and they are not allowed to communicate with anyone else. The team shares a prize if every single person manages to find the box containing their name. **Hint: Utilize the Probability of Success method Question: Suppose the team’s algorithm is the following: each person avoids the box corresponding to their number. Thus, each person selects a different set of 5 boxes. Determine the probability that the team wins the prize by following this algorithm.
Prompt:
A team of six students play the following game. They enter a room one by one in any order until all six of them take their turns. In the room, there is a table with a row of six identical boxes labelled 1, 2, 3, 4, 5, 6 that corressponding to the studunt name. Inside each box is the name of one person, randomly chosen so that each person’s name appears in exactly one box. Once inside the room, each person is allowed to open and look inside 5 boxes of their choice. After each person has opened their five boxes they must leave the room, making sure that the boxes are in exactly the same state as before, and they are not allowed to communicate with anyone else. The team shares a prize if every single person manages to find the box containing their name.
**Hint: Utilize the
Question:
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Suppose the team’s algorithm is the following: each person avoids the box corresponding to their number. Thus, each person selects a different set of 5 boxes. Determine the probability that the team wins the prize by following this algorithm.
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