Lotto App Question

Hi everyone, I've been building an app to show different odds based upon certain constraints. I have most of them worked out but there was one that was too complicated for me. Here it is:

1. Balls: 1-45
2. Six balls drawn
3. All combinations must include either 1 or 2 numbers from 41-45
4. All tickets must be within arrangement 2,2,1,1,0 within each 10 ball range. (example: 2 balls from 1-10, 2 balls from 11-20, 1 ball from 21-30 and 1 ball from 41-45).

What are the odds of getting 3 out of 6, 4 out of 6, 5 out of 6 and 6 out of 6?

A bit tough I know but if the wizard or anyone else can show me the math I would be thankful.

Cheers!

Matt

Two questions:

1. In #3, by "combinations," do you mean the numbers drawn, or the tickets?

2. In #4, does it have to be 2,2,1,1,0 in that order, or just 2 in one "block", 2 in another, 1 in a third, and 1 in a fourth (so, for example, 1, 18, 30, 32, 41, 44 is a valid ticket)?

If the numbers drawn are random (so, for example, 1, 2, 3, 4, 5, 6 can be drawn), and the only restrictions are on the tickets, then the probabilities of winning should be the same regardless of what restrictions exist on the numbers.
There are (45)C(6) = 8,145,060 sets of 6 numbers that can be drawn from 1-45.
To make this easier to visualize, color the 6 balls with your numbers red, and the other 39 white.
There is 1 set of 6 balls that is 6 reds, so the probability of 6/6 is 1 / 8,145,060.
For 5/6, there are (6)C(5) = 6 sets of 5 red balls, and (39)C(1) = 39 sets of 1 white ball, so there are 6 x 39 = 234 combinations of 6 balls with 5 reds; the probability of 5/6 is 234 / 8,145,060 = 1 / 34,807.95
For 4/6, there are (6)C(4) = 15 sets of 4 red balls, and (39)C(2) = 741 sets of 2 white balls, so there are 15 x 741 = 11,115 combinations of 6 balls with 4 reds; the probability of 4/6 is 11,115 / 8,145,060 = 1 / 732.80
For 3/6, there are (6)C(3) = 20 sets of 3 red balls, and (39)C(3) = 9139 sets of 3 white balls, so there are 20 x 9139 = 182,780 combinations of 6 balls with 3 reds; the probability of 3/6 is 182,780 / 8,145,060 = 1 / 44.56

Hi ThatDonGuy :)

1. I meant the number drawn in the lotto. The idea of the app is to show how the odds change depending on if a certain outcome was to occur in the draw guaranteed. For example, if the first number was guaranteed to be 45 then your chances of winning would go up considerably. Like this.

2. The blocks can be in any order. For example it could be 2,2,1,1,0 or 2,1,2,1,0 and so forth. There are thirty combinations of this I believe.

I agree with the math that you provided above, thanks for that. Let me know if you can offer any more insight.

Kind regards,

Matt

I don't think there's an "easy" way to calculate what you are asking for in this case. This is what computers are for.

Here is what I get when I go through every combination of 2 different types of tickets:
Ticket 1 is 1, 2, 11, 12, 21, 41
Ticket 2 is 1, 2, 11, 21, 41, 42
I assume you only want tickets that can get all six numbers

As you can see by the table, Ticket 2 is better, so the probabilities are based on playing Ticket 2

Hits	Ticket 1	Ticket 2	Ticket 2 Prob
0	1304592	1055322
1	1276568	1397808
2	449939	558149
3	69179	87884	1 / 35.33
4	4594	5694	1 / 545.31
5	127	142	1 / 21,866.2
6	1	1	1 / 3,105,000

This is excellent. Thank you so much! Naturally you are right, computers are needed when dealing with the scale of the lotto. Anyway thank you again. ^^

Kind regards,

Matt