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#1 2012-12-20 04:31:42
- cooljackiec
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binomial
how can we prove 2n choose n is always even?
I see you have graph paper.
You must be plotting something
#3 2012-12-20 07:05:52
- bobbym
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Re: binomial
Hi;
I like this proof best:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2012-12-20 09:48:08
- cooljackiec
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Re: binomial
so because i have a 2 * 2n-1 choose n, it is bound to be even?
I see you have graph paper.
You must be plotting something
#5 2012-12-20 09:56:30
- bobbym
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Re: binomial
Hi;
Yes, any integer that is multipled by 2 is even.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#6 2012-12-21 05:05:25
- cooljackiec
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Re: binomial
Another problem:
Consider the polynomial
What are the coefficients of $ f(t-1) $? Enter your answer as an ordered list of four numbers. For example, if your answer were $ f(t-1) = t^3+3t^2-2t+7 $, you'd enter (1,3,-2,7). (This is not the actual answer.)
I see you have graph paper.
You must be plotting something
#7 2012-12-21 05:26:55
- bobbym
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Re: binomial
Hi;
I am getting (1, 3, 3, 1).
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2012-12-21 14:33:22
- cooljackiec
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Re: binomial
thank you. I have another question:
We have 8 pieces of strawberry candy and 7 pieces of pineapple candy. In how many ways can we distribute this candy to 4 kids?
and:
In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?
and:
4 students are running for club president in a club with 50 members. How many different vote counts are possible, if members may choose not to vote?
I see you have graph paper.
You must be plotting something
#9 2012-12-21 15:11:44
- noelevans
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Re: binomial
I'm getting the same as bobbym. It sometimes helps to write the original function in terms of
a different variable than the one you are substituting in its place. For example
f(x) = x^3+6x^2+12x+8 = x^3 + 2*3x^2 + 4*3x + 8 = (x+2)^3
f(x) = (x+2)^3 so f(t-1) = ((t-1)+2)^3 = (t+1)^3 = t^3+3t^2+3t+1 = (1, 3, 3, 1) by replacing
x by t-1 in the f(x) = (x+2)^3.
And as another example find the quadruple for f(t-2).
f(x) = (x+2)^3 so f(t-2) = ((t-2)+2)^3 = t^3 = (3, 0, 0, 0).
These can also be looked at as a composition of functions: f(x)
x+2)^3 and g(x)=x-1.
(fog)(x) = f(g(x)) = f(x-1) = ( (x-1)+2)^3 = (x+1)^3 
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#10 2012-12-21 19:39:17
- bobbym
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Re: binomial
Hi cooljackiec;
4 students are running for club president in a club with 50 members. How many different vote counts are possible, if members may choose not to vote?
I am getting 316251.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#11 2012-12-21 20:07:44
- anonimnystefy
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Re: binomial
On the other hand, I am getting 5^50.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#12 2012-12-21 20:39:53
- bobbym
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Re: binomial
5^50 = 88817841970012523233890533447265625
I bet you did not do a simulation.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#13 2012-12-21 20:42:05
- anonimnystefy
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Re: binomial
Each member has 5 chiloices. There are 50 members, or 46 if you exclude the ones who are running for president. 5 votes per person, 46 persons, 5^46 possible vote counts...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#14 2012-12-21 20:47:03
- bobbym
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Re: binomial
Hi;
Not exactly, If one guy gets 20 votes there are only 30 to spread to the others.
Remember you are only voting for one position not 4.
Take 50 x's and place 3 spacers in various positions.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#15 2012-12-21 21:02:36
- anonimnystefy
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Re: binomial
Actually, you must have 4 spacers...
Your answer is correct.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#16 2012-12-21 21:04:25
- bobbym
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Re: binomial
3 spacers, because you are looking for solutions to
the three spacers make 4 separte groups. Each group is how many is in a variable.
xxxxxxxxxxxxx _ xxxxxxxxxxxxxxxxx _ xxxxxxxxxx _ xxxxxxxxxx
this corresponds to the solution 13 + 17 + 10 + 10 = 50
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#17 2012-12-21 21:38:00
- anonimnystefy
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Re: binomial
There are 5 groups, votes for 1st, 2nd, 3rd and 4th candidate and the non-voters...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#18 2012-12-21 21:42:48
- bobbym
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Re: binomial
The non voters are not a candidate. They are represented by different values of r. For instance when there is one non voter the equation is
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#19 2012-12-21 21:46:37
- anonimnystefy
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Re: binomial
It is easier to look at them as a special category of voters:
where n are the non-voters. There are then .
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#20 2012-12-21 21:53:59
- bobbym
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Re: binomial
Hi;
That is very good, I did not see that. That would get the same answer and there is less calculation.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#21 2012-12-22 05:25:31
- anonimnystefy
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Re: binomial
Exactly!
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#22 2012-12-22 05:30:30
- bobbym
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Re: binomial
Exactly?
There will be times when you will think you or I have found the perfect answer, I assure you these are delusions on your part. - Prof. Kingsfield
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#23 2012-12-22 05:43:26
- anonimnystefy
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Re: binomial
I never said it was perfect... I only agreed that it is much easier to calculate...
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#24 2012-12-22 05:46:06
- bobbym
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Re: binomial
True, but there could be an even easier way...
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#25 2012-12-23 05:17:17
- cooljackiec
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Re: binomial
it is wrong.
I think that it would be 4^50.
Every member has 4 choices. 50 members. But im not sure...
I see you have graph paper.
You must be plotting something