You want to calculate your odds at winning the lottery given:

- You must choose a sequence of 6 numbers correctly to win.
- The lowest number you can choose is 1
- The highest number you can choose is 45
- A given number can only be chosen
onceper try (per lottery ticket, etc.)

When you select your 1 ^{st}number, you have 45 numbers to choose from, and......a 1 in 45 chance of picking the right one.(Mathematically, 1 in 45 is represented by the numerical fraction

or 0.022222.)^{1}/_{45}When you select your 2 ^{nd}number, you have 44 numbers to choose from, and......a 1 in 44 chance of picking the right one.(Mathematically, 1 in 44 is represented by the numerical fraction

or 0.022727.)^{1}/_{44}When you select your 3 ^{rd}number, you have 43 numbers to choose from, and......a 1 in 43 chance of picking the right one.(Mathematically, 1 in 43 is represented by the numerical fraction

or 0.023256.)^{1}/_{43}When you select your 4 ^{th}number, you have 42 numbers to choose from, and......a 1 in 42 chance of picking the right one.(Mathematically, 1 in 42 is represented by the numerical fraction

or 0.023810.)^{1}/_{42}When you select your 5 ^{th}number, you have 41 numbers to choose from, and......a 1 in 41 chance of picking the right one.(Mathematically, 1 in 41 is represented by the numerical fraction

or 0.024390.)^{1}/_{41}When you select your 6 ^{th}number, you have 40 numbers to choose from, and......a 1 in 40 chance of picking the right one.(Mathematically, 1 in 40 is represented by the numerical fraction

or 0.025000.)^{1}/_{40}In order to win, you have to pick the first number right AND the second number right AND the third number right, etc. In the language of statistics, AND usually means tomultiply.So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.

^{1}/_{45}×^{1}/_{44}×^{1}/_{43}×^{1}/_{42}×^{1}/_{41}×^{1}/_{40}=^{1}/_{5864443200}So, at this point, your odds of winning are 1 in 5864443200. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 6 numbers can be written down, which for 6 numbers is 6! (6 factorial) or 720. Divide 5864443200 by 720 to account for this, to get 8145060.

In other words, there are 720 different ways that the 6 numbers you choose can be filled out on your lottery ticket--if you choose your 6 numbers correctly, any of these ways will make a winning ticket.

That's it! You have a 1 in 8,145,060

chance of winning the lottery you described.

Here are some other odds for the sake of comparison:

- You have about a 1 in 2,000,000 chance of being struck by lightning.
- A pregnant woman has a 1 in 705,000 chance of giving birth to quadruplets.
- Someone eating an oyster has a 1 in 12,000 chance of finding a pearl inside of it.
Good luck! And sorry to say that the only way to increase your chances of winning is

to buy more tickets!Choosing birthdays, your age, addresses, years, phone numbers, etc. does not help at all!