My question is the next.

We imagine I want to play to Powerball.
I know we must to choose 5 numbers among 69 numbers (From 1 to 69. Color of these balls is white) and another one among 26 (Numbered 1 to 26. Color of these balls is red).

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) ?

(January 3, 2022 at 9:36 am)viocjit Wrote: My question is the next.

We imagine I want to play to Powerball.
I know we must to choose 5 numbers among 69 numbers (From 1 to 69. Color of these balls is white) and another one among 26 (Numbered 1 to 26. Color of these balls is red).

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)  ?

There are three types of mathematician: those who can count and those who can't.

(January 3, 2022 at 9:57 am)polymath257 Wrote:

(January 3, 2022 at 9:36 am)viocjit Wrote: My question is the next.

We imagine I want to play to Powerball.
I know we must to choose 5 numbers among 69 numbers (From 1 to 69. Color of these balls is white) and another one among 26 (Numbered 1 to 26. Color of these balls is red).

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)  ?

There are three types of mathematician: those who can count and those who can't.

Good joke ! You haven't any idea how to make the calculation I want ?

(January 11, 2022 at 10:50 am)viocjit Wrote:

(January 3, 2022 at 9:57 am)polymath257 Wrote: There are three types of mathematician: those who can count and those who can't.

Good joke ! You haven't any idea how to make the calculation I want ?

Does the order of the numbers matter? For example, is the sequence 24-32-56 treated in a different way than 32-56-23?

Apart from that ambiguity, this is a simple combinatorics problem.

(January 11, 2022 at 11:34 am)polymath257 Wrote:

(January 11, 2022 at 10:50 am)viocjit Wrote: Good joke ! You haven't any idea how to make the calculation I want ?

Does the order of the numbers matter? For example, is the sequence 24-32-56 treated in a different way than 32-56-23?

Apart from that ambiguity, this is a simple combinatorics problem.

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.

(January 17, 2022 at 12:05 am)viocjit Wrote:

(January 11, 2022 at 11:34 am)polymath257 Wrote: Does the order of the numbers matter? For example, is the sequence 24-32-56 treated in a different way than 32-56-23?

Apart from that ambiguity, this is a simple combinatorics problem.

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.

A necessary, but not sufficient, condition to be an employable mathematician is to be a prodigy.

(January 19, 2022 at 4:28 pm)Jehanne Wrote: A necessary, but not sufficient, condition to be an employable mathematician is to be a prodigy.

Neither necessary nor sufficient, but helpful.

(January 19, 2022 at 7:30 pm)polymath257 Wrote:

(January 19, 2022 at 4:28 pm)Jehanne Wrote: A necessary, but not sufficient, condition to be an employable mathematician is to be a prodigy.

Neither necessary nor sufficient, but helpful.

If only Donald Trump could be so modest...

The NFL began sharing a new statistic this year that I had never even thought about and it is blowing my mind. They've announced several times when final game scores are unique within the existence of the NFL. Example, when the Colts beat the the Bills 41 - 15 this year, this was the first time this final score had ever been recorded in the NFL. They call it a Scorigami. With the addition of the 2 point conversion and moving the extra point back 15 yards, I can see how this is opening up the range of scores because we now get less common combinations than we used to. Scores were once almost totally limited to combinations of 3, 6 or 7, with a very rare 2 pointer for a safety. But now we often get the 2 point conversion and more often get 6 points due to missed extra points. Still, I'm amazed that some of these combinations have never been recorded.