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Comibatorics Question with Scenarios

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Retired Moderator
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Comibatorics Question with Scenarios [#permalink]

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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]

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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

Kudos [?]: 61 [0], given: 2

Senior Manager
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Joined: 01 Feb 2010
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Re: Comibatorics Question with Scenarios [#permalink]

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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.

Kudos [?]: 61 [0], given: 2

Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1292

Kudos [?]: 1218 [0], given: 157

Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
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Re: Comibatorics Question with Scenarios [#permalink]

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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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Kudos [?]: 1218 [0], given: 157

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Re: Comibatorics Question with Scenarios [#permalink]

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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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Kudos??

Kudos [?]: 260 [0], given: 260

Senior Manager
Senior Manager
avatar
Joined: 01 Feb 2010
Posts: 251

Kudos [?]: 61 [0], given: 2

Re: Comibatorics Question with Scenarios [#permalink]

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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

Kudos [?]: 61 [0], given: 2

Senior Manager
Senior Manager
User avatar
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 290

Kudos [?]: 260 [0], given: 260

Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
GMAT ToolKit User Premium Member
Re: Comibatorics Question with Scenarios [#permalink]

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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.
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Kudos [?]: 260 [0], given: 260

Re: Comibatorics Question with Scenarios   [#permalink] 24 Mar 2010, 23:22
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Comibatorics Question with Scenarios

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