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

When you select your 1st 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 1/45 or 0.022222.)

When you select your 2nd 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 1/44 or 0.022727.)

When you select your 3rd 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 1/43 or 0.023256.)

When you select your 4th 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 1/42 or 0.023810.)

When you select your 5th 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 1/41 or 0.024390.)

When you select your 6th 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 1/40 or 0.025000.)

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 to multiply.

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.

(How do I pronounce this number?)

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!