At the beginning of the semester, we guessed the odds of winning the CA Super Lotto (my guess was 1 in a million chance).
The rules are simple: 1. Choose any 5 numbers between 147 (these numbers will not be repeated) 2. Pick a mega number between 127 (this number may repeat) 3. Match all 5 numbers and the mega number and you win! We then played it and used a number generator, and realized the odds of winning are very low. This leaded on to our 3 questions:
1.) How many different number combinations are possible for a CA Super Lotto ticket? 2.) What is the propability of winnning the CA Super Lotto? 3.) If you match all 6 numbers, you win $8,000,000. It costs $1 to play. WHat are your expected winnings? 
You have to choose 5 numbers between 147 (does not repeat), and pick a mega number between 127 (may repeat). So instead of multiplying 47^5, it would be 47*46*45*44*43 because every time, you are removing a number from the total=47 to be one out of the 5 numbers your pick. Then the total would be 46, and from this remove another number...etc. I also multiplied 27 because the number can be repeated when chosen.

To win you have to match all 5 numbers and the mega number. The denominators is the sample space, which we have done in the first questions, the numerator is how many numbers are left. So there it is 5/47 because 5 numbers need to be picked from the total amounts of numbers=47. Then it is 4/46 because 1 number has been picked so instead of 5 numbers now it would be 4 numbers you need to pick...etc. It is 1/27 because it is only 1 mega number from the total=27. Then once I multiplied all those I got 120/4,969,962,360 which can be simplified down.

To find the expected winnings I used the expected value formula and plugged all the information I had in. So( $8,000,000) is how much you will get if you win * the probability of winning, which was (120 / 4,969,962,360), then you add the probability of losing which is (1) (4,969,962,240 / 4,969,962,360). Then once you solve it and round the decimal, you lose .81 cents with each Lotto ticket you buy.
