mathdaemon
New member
- Joined
- Dec 26, 2012
- Messages
- 35
Hello everyone,
I am a bit confused as to how to solve problems based on ordered and unordered partitions in Cominatorics.
Ok, so I have two questions
1) How many ways can 10 persons be divided into 3 teams such that Team-1 contains 3, Team-2 contains 2 and Team-3 contains 5 members respectively?
The answer to this is 10!/(3! X 2! X 5!). This can be obtained from the permutations with repeatition formula n!/(a! X b! X c!...).
I don't understand how this formula can be used here because persons are distinct.
2) How many ways can 10 persons be divided into 5 teams of 2 each?
My incorrect solution is .... 1st team chosen in 10 X 9 ways, 2nd in 8 X 7 ways and so on.
Why is the solution incorrect.
What should be the logic of the correct solution(10! / (5 X 2! X 5!))
3) In the solution above 5! is for arranging teams among themselves in five ways.
Is the same logic valid if in question 1) the sizes of 2(or more) teams are the same?
I hope my questions are understandable.
Please do help.
Thanks in advance
I am a bit confused as to how to solve problems based on ordered and unordered partitions in Cominatorics.
Ok, so I have two questions
1) How many ways can 10 persons be divided into 3 teams such that Team-1 contains 3, Team-2 contains 2 and Team-3 contains 5 members respectively?
The answer to this is 10!/(3! X 2! X 5!). This can be obtained from the permutations with repeatition formula n!/(a! X b! X c!...).
I don't understand how this formula can be used here because persons are distinct.
2) How many ways can 10 persons be divided into 5 teams of 2 each?
My incorrect solution is .... 1st team chosen in 10 X 9 ways, 2nd in 8 X 7 ways and so on.
Why is the solution incorrect.
What should be the logic of the correct solution(10! / (5 X 2! X 5!))
3) In the solution above 5! is for arranging teams among themselves in five ways.
Is the same logic valid if in question 1) the sizes of 2(or more) teams are the same?
I hope my questions are understandable.
Please do help.
Thanks in advance
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