When you select your 1st number, you have 99 numbers to choose from, and…
...a 1 in 99 chance of picking the right one.
(Mathematically, 1 in 99 is represented by the numerical fraction 1/99 or 0.010101.)
When you select your 2nd number, you have 98 numbers to choose from, and…
...a 1 in 98 chance of picking the right one.
(Mathematically, 1 in 98 is represented by the numerical fraction 1/98 or 0.010204.)
When you select your 3rd number, you have 97 numbers to choose from, and…
...a 1 in 97 chance of picking the right one.
(Mathematically, 1 in 97 is represented by the numerical fraction 1/97 or 0.010309.)
When you select your 4th number, you have 96 numbers to choose from, and…
...a 1 in 96 chance of picking the right one.
(Mathematically, 1 in 96 is represented by the numerical fraction 1/96 or 0.010417.)
When you select your 5th number, you have 95 numbers to choose from, and…
...a 1 in 95 chance of picking the right one.
(Mathematically, 1 in 95 is represented by the numerical fraction 1/95 or 0.010526.)
When you select your 6th number, you have 94 numbers to choose from, and…
...a 1 in 94 chance of picking the right one.
(Mathematically, 1 in 94 is represented by the numerical fraction 1/94 or 0.010638.)
When you select your 7th number, you have 93 numbers to choose from, and…
...a 1 in 93 chance of picking the right one.
(Mathematically, 1 in 93 is represented by the numerical fraction 1/93 or 0.010753.)
When you select your 8th number, you have 92 numbers to choose from, and…
...a 1 in 92 chance of picking the right one.
(Mathematically, 1 in 92 is represented by the numerical fraction 1/92 or 0.010870.)
When you select your 9th number, you have 91 numbers to choose from, and…
...a 1 in 91 chance of picking the right one.
(Mathematically, 1 in 91 is represented by the numerical fraction 1/91 or 0.010989.)
When you select your 10th number, you have 90 numbers to choose from, and…
...a 1 in 90 chance of picking the right one.
(Mathematically, 1 in 90 is represented by the numerical fraction 1/90 or 0.011111.)
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.
1/99 × 1/98 × 1/97 × 1/96 × 1/95 × 1/94 × 1/93 × 1/92 × 1/91 × 1/90 = 1/56534085859976527872
So, at this point, your odds of winning are 1 in 56534085859976527872. 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 10 numbers can be written down, which for 10 numbers is 10! (10 factorial) or 3628800. Divide 56534085859976527872 by 3628800 to account for this, to get 15579278510796.
In other words, there are 3628800 different ways that the 10 numbers you choose can be filled out on your lottery ticket--if you choose your 10 numbers correctly, any of these ways will make a winning ticket.