I must Compute the number of ways in which complicated events can occur without actually counting them through the use of the fundamental counting principle, permutations, combinations, tree diagrams, and tables;

compute probabilities, odds, and expected values of outcomes

HOW TO PLAY HIT 5

• Select 5 numbers between 1 and 42 or let the computer Quick Pick random numbers.
• Each play is $1.
• There are four ways to win!
• Win all the money all at once.
• The Cashpot starts at $100,000 and keeps rolling until someone wins.

5 White Balls	CASHPOT*	1 in 851 Thousand
4 White Balls	$150	1 in 4.60 Thousand
3 White Balls	$15	1 in 128
2 White Balls	FREE HIT 5 TICKET	1 in 11.0

What is the total amount of numbers involved? To win, how many numbers must be chosen? Is there a unique number included in the package? Are there any other prizes if you only have a few of the correct numbers?

Determine the number of elements in the lottery sample space. (by using there are a lot of various permutations/combinations of numbers.) If you can please explain the work in digital form

One of my classmates helped me and showed me her results and how she came up with the answer it looked like this

This shows the combination for choosing 5 numbers out of 39 where the order doesn't matter.

So 39!/(39-5)!5! can be simplified to 69090840/5! which is equal to 575,757. So your chances of winning this jackpot is 1/575,757 which aren't terrible. However, the jackpot is much smaller, and given the better chances of winning, you'll likely be splitting the jackpot with others.