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Comibatorics Question with Scenarios

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Hussain15
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Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 10:29
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A men's basket ball team assigns every player a two digit number for the back of his jersey. If the digit uses the digits 1 to 5, what is the maximum number of players that can join the league such that no player has a number with repeated digits (like 22) & no two players have the same number??

Guys, after answering the above question, kindly consider the following scenarios:

Scenario 1: What will be the answer, if the repetition (eg 22) is allowed.

Scenario 2: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is not allowed.

Scenario 3: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is allowed.

Well, I think if I can get some views on these scenarios, I can understand "Combinatorics". These scenarios emerged as a result of a discussion between myself & AtifS (an active member of the club & my partner).

The source of question is MGMAT Guide while the 3 scenarios are our creation.



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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 10:46
Hussain15 wrote:
A men's basket ball team assigns every player a two digit number for the back of his jersey. If the digit uses the digits 1 to 5, what is the maximum number of players that can join the league such that no player has a number with repeated digits (like 22) & no two players have the same number??
The source of question is MGMAT Guide while the 3 scenarios are our creation.


1st digit = 5 ways
2nd digit = 4 ways
total = 5*4 = 20 players

Please mention the OA
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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 10:49
Hussain15 wrote:
A men's basket ball team assigns every player a two digit number for the back of his jersey. If the digit uses the digits 1 to 5, what is the maximum number of players that can join the league such that no player has a number with repeated digits (like 22) & no two players have the same number??
Guys, after answering the above question, kindly consider the following scenarios:
Scenario 1: What will be the answer, if the repetition (eg 22) is allowed.
Scenario 2: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is not allowed.
Scenario 3: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is allowed.
The source of question is MGMAT Guide while the 3 scenarios are our creation.

Scenario1: if repetition allowed then its 5 * 5 = 25 players.

Scenario 2: 5 * 4 * 3 = 60 players.

Scenario 3: 5 * 5 * 5 = 125 players.
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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 12:14
Thanks for the input, official answer will be shared soon after a few inputs.

Posted from my mobile device
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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 12:15
bangalorian2000 wrote:
Hussain15 wrote:
A men's basket ball team assigns every player a two digit number for the back of his jersey. If the digit uses the digits 1 to 5, what is the maximum number of players that can join the league such that no player has a number with repeated digits (like 22) & no two players have the same number??
Guys, after answering the above question, kindly consider the following scenarios:
Scenario 1: What will be the answer, if the repetition (eg 22) is allowed.
Scenario 2: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is not allowed.
Scenario 3: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is allowed.
The source of question is MGMAT Guide while the 3 scenarios are our creation.

Scenario1: if repetition allowed then its 5 * 5 = 25 players.

Scenario 2: 5 * 4 * 3 = 60 players.

Scenario 3: 5 * 5 * 5 = 125 players.

Nice! can you please! explain y did you take 5*5=5^2 for 1st scenario and y did you take 5*5*5=5^3 for 3rd scenario? I just wanted to know the logic behind t. Well I think 5 options are possible for 1st digit and similarly 5 for 2nd digit. Same goes for 3-digit number. But would like to know your explanation as there might be anything useful to know :)
Thanks,

-A
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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 21:50
AtifS wrote:
bangalorian2000 wrote:
Hussain15 wrote:
A men's basket ball team assigns every player a two digit number for the back of his jersey. If the digit uses the digits 1 to 5, what is the maximum number of players that can join the league such that no player has a number with repeated digits (like 22) & no two players have the same number??
Guys, after answering the above question, kindly consider the following scenarios:
Scenario 1: What will be the answer, if the repetition (eg 22) is allowed.
Scenario 2: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is not allowed.
Scenario 3: What will be the answer, if every player is assigned a "three" digit number from the digits 1 to 5 & the repetition of digits (eg 323 or 333) is allowed.
The source of question is MGMAT Guide while the 3 scenarios are our creation.

Scenario1: if repetition allowed then its 5 * 5 = 25 players.

Scenario 2: 5 * 4 * 3 = 60 players.

Scenario 3: 5 * 5 * 5 = 125 players.

Nice! can you please! explain y did you take 5*5=5^2 for 1st scenario and y did you take 5*5*5=5^3 for 3rd scenario? I just wanted to know the logic behind t. Well I think 5 options are possible for 1st digit and similarly 5 for 2nd digit. Same goes for 3-digit number. But would like to know your explanation as there might be anything useful to know :)
Thanks,

-A


The logic is same as you said,
if digit repeat is allowed than
ways to select 1st digit = 5 (either of 1,2,3,4,5)
ways to select 2nd digit = 5 (either of 1,2,3,4,5)
total = 5*5 = 25

for the case when number on player's shirt is of three digits then
ways to select 1st digit = 5 (either of 1,2,3,4,5)
ways to select 2nd digit = 5 (either of 1,2,3,4,5)
ways to select 3rd digit = 5 (either of 1,2,3,4,5)
total = 5*5*5 = 125
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Re: Comibatorics Question with Scenarios [#permalink] New post   24 Mar 2010, 23:22
@bangalorian!
Now that's better :) even a newbie can understand that's why I asked you to explain it because others can understand it easily.
P.S: Actually! I did have idea after discussion with Hussain15 but wasn't sure and also wanted others views.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Comibatorics Question with Scenarios [#permalink]
24 Mar 2010, 23:22
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