30Oct

The Lottery Mathematics

One of the most popular forms of gambling is the Lottery. Unfortunately, some people do not realize the sheer amount of luck you would have to have to win the lottery. With our skills in Combinations, though, we can find out just how lucky you have to be to win that \$3 million dollars.

What is the Lottery in the first place?

The Lottery is a game, usually run by the government, where people choose a number of numbers out of a certain set and then hope to match them when the numbers are announced later. For example, a very small lottery might have you choose three numbers between 1 and 10. If you chose 3, 5, and 2 and the winning numbers were 5, 3 and 2, you would win the prize. Order does not matter, though, making the number of combinations of numbers a combination, not a permutation.

So what’s the chance of winning the Florida Lottery?

The Florida Lottery is the biggest single state lottery in the country. In the game you must choose six numbers between one and fifty three. If you match them all, you win!

So just how many ways can you pick six numbers?

First, we need to recall our formula for combinations.

C=n!/r!(n-r)!

Then we fill in our values for n, fifty three, and r, 6 (Because there are 53 numbers to choose from and we choose 6)

C=53!/6!(53-6)!

C=53!/6!(47)!

You can easily council out the 47! by taking the numbers from 53! until you reach 47.

C=53*52*51*50*49*48/6*5*4*3*2*1

C= 16,529,385,600/720

C= 22,957,480

So there are 22,957,480 ways to choose 6 numbers. If you buy one ticket, your chance of winning is one in 22,957,480, or approximately .000004%.

Sure, that’s very small, but just HOW small? The chance of being hit by lightning, a very small chance, is one in 35,000, making being hit by lightning 655 times MORE likely than winning the lottery.

Of course, you can buy multiple lottery tickets. If you bought one ticket for every drawing- they draw twice a week- it would take you 220,745 YEARS to have a statistical chance of 100% of winning. You could also buy 22,957,480 tickets, but only rarely does the jackpot get over 22 million dollars, and then the chance of being the only winner is very very small. Of course there are other prizes (we only found the chance of winning the jackpot).