My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 6th, 2013, 01:05 AM   #1
 
Joined: Apr 2013

Posts: 4
Thanks: 0

Question in combinatorics

Hello all
I had an exercise in maths that said:
4 Greeks, 6 Russians and 3 Albanians are candidates of a 4 member group, but in that group all these 3 nationalities must be present. The teacher said that we must separate the problem in 3 cases:
1st: we take 2 Greeks and 1 of each of the others
2nd: we take 2 Russians and 1 of each of the others
3rd: we take 2 Albanians and 1 of each of the others

I tried to solve it by separating it in 2 cases:
We take 1 of each nationality
We take 1 of the 10 people that remain (subtract 1 of each and add them together

But the answer was wrong, actually was 2 times the correct one.
I didn't quite understand my teacher's explanation. Can someone explain why my method is wrong?
Thank you
michaelg9 is offline  
 
April 6th, 2013, 02:21 AM   #2
Math Team
 
Joined: Nov 2010
From: Greece, Thessaloniki

Posts: 1,965
Thanks: 123

Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus
Re: Question in combinatorics

1st.
2nd
3rd
[color=#000000]
What is the result you get?[/color]
ZardoZ is offline  
April 6th, 2013, 03:01 AM   #3
 
Joined: Apr 2013

Posts: 65
Thanks: 0

Re: Question in combinatorics

At the second case you actually do a permutation. So you have to divide it by 2!
Drake is offline  
April 6th, 2013, 03:05 AM   #4
 
Joined: Apr 2013

Posts: 4
Thanks: 0

Re: Question in combinatorics

That's my teacher's method, however at the 3rd part it's 4 x 3 x 6=72 so the total of the 3 parts is 360. That's the correct solution
However, with my method I get a total of 720.
Why?
michaelg9 is offline  
April 6th, 2013, 03:10 AM   #5
 
Joined: Apr 2013

Posts: 4
Thanks: 0

Re: Question in combinatorics

@Drake: why am I doing a permutation? I am using the 10C1 formula. Can you explain please?
Thanks
michaelg9 is offline  
April 6th, 2013, 04:13 AM   #6
 
Joined: Apr 2013

Posts: 65
Thanks: 0

Re: Question in combinatorics

Well, the fourth person will be from the same nation with one of the 3. Let me give an example:

and are same group, but you count them twice.
Drake is offline  
April 6th, 2013, 11:07 AM   #7
 
Joined: Apr 2013

Posts: 4
Thanks: 0

Re: Question in combinatorics

Hmm now I see... So I had to devide by 2!
Thank you for the help!
michaelg9 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
combinatorics, question



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Combinatorics question rummi Advanced Statistics 0 January 16th, 2013 02:58 PM
Combinatorics QUESTION 1-3 maximus101 Applied Math 1 October 22nd, 2012 03:58 AM
Combinatorics QUESTION maximus101 Number Theory 1 October 21st, 2012 04:28 PM
Combinatorics QUESTION 3-3 maximus101 Applied Math 1 October 20th, 2012 01:05 PM
Combinatorics question proglote Algebra 3 May 1st, 2011 06:06 AM





Copyright © 2014 My Math Forum. All rights reserved.