Fred is the owner of 10 original Fabergé Eggs. He has a display case like the one below, and he...

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Fred is the owner of 10 original Fabergé Eggs. He has a display case like the one below, and he rearranges the eggs each week. How long will it be before Fred has to repeat an arrangement? (b) Hoping to get a big tax write-off, Fred decides to donate 5 of his Fabergé eggs to a museum. The curator decides to put 3 of them on display at a time, one next to the other as above, and to rearrange the display each week. If Fred visits his donation each week, how long before he’ll have to see a repeated display? Basketball Teams: Fred and 4 of his friends put together a team for a half-court basketball tournament. (Fred is, naturally, the player-coach.) During each game, three people play at a time and unlimited substitutions are allowed. How many different three-person teams could Fred put on the court during the course of a game? (a) Recount strategies and solutions to the three tasks offered in

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1 Final Re-Cap In the last few classes we have solved these problems: Fabergé Eggs: (a) Fred is the owner of 10 original Fabergé Eggs. He has a display case like the one below, and he rearranges the eggs each week. How long will it be before Fred has to repeat an arrangement? (b) Hoping to get a big tax write-off, Fred decides to donate 5 of his Fabergé eggs to a museum. The curator decides to put 3 of them on display at a time, one next to the other as above, and to rearrange the display each week. If Fred visits his donation each week, how long before he’ll have to see a repeated display? Basketball Teams: Fred and 4 of his friends put together a team for a half-court basketball tournament. (Fred is, naturally, the player-coach.) During each game, three people play at a time and unlimited substitutions are allowed. How many different three-person teams could Fred put on the court during the course of a game? (a) Recount strategies and solutions to the three tasks offered in class. (Remember, several different approaches were used to solve part (b) of the Fabergé Eggs task.) (b) Discuss ways in which these tasks are similar, ways in which they are different, and how these similarities and differences help connect the strategies and solutions you discuss in part (a). Metro State MTH 1610 Integrated Mathematics I

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Robert · Accepted Answer

Ans.
(a)  
No. of original eggs, 
10 eggs  
No. of possible arranges for the eggs, 
10! 
 The owner changes the arrangement each week so the no. of week taken to repeat the 
arranges will be no. of possible arrangements. 
 So, the maximum possible arrangements, 3628800week .
(b)  
No. of eggs donated to museum, 
5eggs  
In the museum the arrangement of boxes are same means it has 10 spaces. But the 
curator decides to put 3 eggs at each time and in alternate method. There is a blank 
box between the two places.
So the number of places to put the eggs, 
6Places  
The number of eggs to put in them, 
3eggs   
The possible arrangement for the 1
st
 egg will be 6, for second egg will be 5, for third 
egg will be 4. These are independent to each other so the overall arrangements will be, 
6
3
6! 6 5 4 3!
120
3! 3!
P
  
  
Hence, the curator changes the arrangement on each week, so the possible 
weeks will be equal to number of possible arrangements. After the all possible 
arrangements the arrangement will repeat to its first arrangement.
Since the order is fixed so the changes will be in fixed order. Hence, the owner 
had seen the repeated arrangement before 120 weeks.
Note-The above mentioned cases can be changed if the eggs are not distinct. The 
arrangements are valid if and only if the eggs are distinct.

Fred is the owner of 10 original Fabergé Eggs. He has a display case like the one below, and he rearranges the eggs each week. How long will it be before Fred has to repeat an arrangement? (b) Hoping...

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