Ask a Mathematician

[no one]

If 6, turned out to be 9, would you mind?

[polymath257]

If 6, turned out to be 9, would you mind?

Only when the wind whispers Mary.

[viocjit]

The order of the numbers isn't a problem. It can be in any order.
I don't know anything or nearly nothing in combinatorics problem for PowerBall or any other lottery.

We imagine I want to play with 3 white numbers that are even and 2 white who are odd or 3 white numbers that are odd and 2 white even.
Also, I want to choose three numbers between 1 and 34 and two between 35 and 69 or three number between 35 and 69 and two between 1 and 34.

How calculate how many combinations I can play with 3 even and 2 odd (I have the same question for the reverse) and three between 1 and 34 then two between 35 and 69 (I have the same question for the reverse) ?

I don't know how to calculate the numbers of combinations with the limitations of my choice.
The limitations of my choice are those previously said in this message.

OK, I'll take you through one of the problems. The rest are done in a similar way.

First, there are 35 odd and 34 even numbers between 1 and 69. There are 13 odd and 13 even numbers between 1 and 26.

So, suppose you want 3 odd numbers and 2 even numbers between 1 and 69. I assume that order doesn't matter and no number can be repeated.

Then, there are 35*34*33 *ordered* ways to pick 3 odd numbers. Divide this by 3*2*1 ways of permuting those and we get 35*34*33/(3*2*1) ways to pick 3 even numbers between 1 and 69.

For the even, you will have 34*33/(2*1) possible ways.

Multiply these two numbers to get the total number of ways of picking 3 odd and 2 even numbers from 1 to 69:

(35*34*33/(3*2*1) * 34*33/(2*1) = 3561745 ways of picking white balls in this scenario.

You still need to pick the red balls, and if you only pick one, there are 26 ways t . So multiply
all together to find

3671745*26=9546370 ways.

This, by the way, will be the same as picking 3 balls from 35-69 (35 possibilities) and 2 from (1-34) (34 possibilities) and then one red ball.

By the way, this isn't mathematics as it is done today. You could have easily looked up the process online.

Thanks to had take time to answer me !

(35*34*33/(3*2*1) * 34*33/(2*1) I get with my calculator the next result : 3671745 but you get 3561745.
Numbers in bold indicate the different numbers in ours results.

[GrandizerII]

OK, I'll take you through one of the problems. The rest are done in a similar way.

First, there are 35 odd and 34 even numbers between 1 and 69. There are 13 odd and 13 even numbers between 1 and 26.

So, suppose you want 3 odd numbers and 2 even numbers between 1 and 69. I assume that order doesn't matter and no number can be repeated.

Then, there are 35*34*33 *ordered* ways to pick 3 odd numbers. Divide this by 3*2*1 ways of permuting those and we get 35*34*33/(3*2*1) ways to pick 3 even numbers between 1 and 69.

For the even, you will have 34*33/(2*1) possible ways.

Multiply these two numbers to get the total number of ways of picking 3 odd and 2 even numbers from 1 to 69:

(35*34*33/(3*2*1) * 34*33/(2*1) = 3561745 ways of picking white balls in this scenario.

You still need to pick the red balls, and if you only pick one, there are 26 ways t . So multiply
all together to find

3671745*26=9546370 ways.

This, by the way, will be the same as picking 3 balls from 35-69 (35 possibilities) and 2 from (1-34) (34 possibilities) and then one red ball.

By the way, this isn't mathematics as it is done today. You could have easily looked up the process online.

Thanks to had take time to answer me !

(35*34*33/(3*2*1) * 34*33/(2*1) I get with my calculator the next result : 3671745 but you get 3561745.
Numbers in bold indicate the different numbers in ours results.

He uses the correct result later on, so not too big a problem.

[polymath257]

OK, I'll take you through one of the problems. The rest are done in a similar way.

First, there are 35 odd and 34 even numbers between 1 and 69. There are 13 odd and 13 even numbers between 1 and 26.

So, suppose you want 3 odd numbers and 2 even numbers between 1 and 69. I assume that order doesn't matter and no number can be repeated.

Then, there are 35*34*33 *ordered* ways to pick 3 odd numbers. Divide this by 3*2*1 ways of permuting those and we get 35*34*33/(3*2*1) ways to pick 3 even numbers between 1 and 69.

For the even, you will have 34*33/(2*1) possible ways.

Multiply these two numbers to get the total number of ways of picking 3 odd and 2 even numbers from 1 to 69:

(35*34*33/(3*2*1) * 34*33/(2*1) = 3561745 ways of picking white balls in this scenario.

You still need to pick the red balls, and if you only pick one, there are 26 ways t . So multiply
all together to find

3671745*26=9546370 ways.

This, by the way, will be the same as picking 3 balls from 35-69 (35 possibilities) and 2 from (1-34) (34 possibilities) and then one red ball.

By the way, this isn't mathematics as it is done today. You could have easily looked up the process online.

Thanks to had take time to answer me !

(35*34*33/(3*2*1) * 34*33/(2*1) I get with my calculator the next result : 3671745 but you get 3561745.
Numbers in bold indicate the different numbers in ours results.

Yes, it is 3671745. I read the calculator wrong. Sorry.

[vulcanlogician]

Is math identical with logic?

If not, what distinguishes the two?

[polymath257]

Is math identical with logic?

If not, what distinguishes the two?

There are a number of differences.

For example, the study of logic.al fallacies (ad hom, etc) would not be considered a part of mathematics. It is often considered to be a part of logic, however.

On the other hand, *formal* logic can be considered a topic in mathematics: it is the study of a formal system. So, Russell and Whitehead were doing both logic and math when they wrote Principia Mathemtica.

Typically, the distinction between logic and math is placed in such a way that logic gets the propositional and quantifier calculus and the study of equality and math begins when sets are considered.

Even so, there is a lot of overlap between logic and the foundations of math. Godel is usually regarded as a logician, for example, even though he studied set theory and model theory. By the time of Cohen and Shelah, though, set theory and model theory were seen as definitively inside of math.

On the flip side, topics like abstract algebra, topology, differential geometry, etc, are never considered to be part of logic, even when they enter into the arguments for set theory or model theory.

[Fireball]

Why "257"? Were the lower versions already used?

[polymath257]

Why "257"? Were the lower versions already used?

It is a Fermat prime. There are only 5 such known: 3, 5, 17, 257, 65537.

And yes, 3, 5, and 17 tend to be taken.

Fermat primes have a very deep connection with which polygons can be constructed by straightedge and compass as well as other aspects of algebraic number theory.

[vulcanlogician]

Is math identical with logic?

If not, what distinguishes the two?

There are a number of differences.

For example, the study of logic.al fallacies (ad hom, etc) would not be considered a part of mathematics. It is often considered to be a part of logic, however.

On the other hand, *formal* logic can be considered a topic in mathematics: it is the study of a formal system. So, Russell and Whitehead were doing both logic and math when they wrote Principia Mathemtica.

Typically, the distinction between logic and math is placed in such a way that logic gets the propositional and quantifier calculus and the study of equality and math begins when sets are considered.

Even so, there is a lot of overlap between logic and the foundations of math. Godel is usually regarded as a logician, for example, even though he studied set theory and model theory. By the time of Cohen and Shelah, though, set theory and model theory were seen as definitively inside of math.

On the flip side, topics like abstract algebra, topology, differential geometry, etc, are never considered to be part of logic, even when they enter into the arguments for set theory or model theory.

Yeah Godel is who I had in mind when I asked. Because he tried (and failed) to unite the two. I might be oversimplifying here... not too familiar with Godel's work...

But I now realize I mis-worded my question. Maybe I should have asked: "Treated strictly, should logic be considered part of math?" Logical fallacies needn't be included because that's more so about the foibles of our human brains. And things like geometry needn't be considered logic.

Aside from thinking of Godel, I was thinking that some discrete mathematics reminds me of logic, while symbolic logic reminds me of math.