Lottery - to play...or not to play....

Many people dream of what they would do if they hit the lottery. But what are your chances? Here is the math behind the game.

The lottery is considered to be a "combination" - a probability term that indicates you are choosing from a group, where order does not matter. In other words, the lottery "sees" the numbers 5, 10, 15, 10, 25 the same as it sees 10, 5, 15, 20, 25 or any other combination of those same five numbers. So you have to divide all of the redundancies from the total possibilities. So here is how it works. There are 56 numbered balls and 5 are chosen. So there are 56*55*54*53*52 possible comibinations. There is also a bonus ball, of which there are 46 possible. But you have to divide out all of the redundancies. This is done by dividing by 5*4*3*2*1. This gives you 175,711,536. Therefore there are about 176,000,000 different number combinations.

Lets look at a simple example. Consider the number 1, 2, 3, 4. You want to see how many possible combinations there are to pick 2 numbers. So here is the list:

1 and 2, 1 and 3, 1 and 4, 2 and 1, 2 and 3, 2 and 4, 3 and 1, 3 and 2, 3 and 4, 4 and 1, 4 and 2, 4 and 3

But some of the combinations are repeats, and therefore are not considered in combination problems where the order of the numbers does not matter. There are 6 of the 12 as redundancies. The first number there are 4 possible picks and the second number has 3 possible picks, this gives 4*3 = 12 arrangements, but you have to divide by the mulitple of redundancies, which is 2 in this case.

Hope this makes sense. So, in order to guarantee winnning the lottery, fill out 176,000,000 tickets with each combinations....think you have the time?  What would you do with your winnings?