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 Subject: Math Problem College level Category: Reference, Education and News > Education Asked by: arturo-ga List Price: \$22.00 Posted: 12 Oct 2003 08:28 PDT Expires: 11 Nov 2003 07:28 PST Question ID: 265431
 ```Class is called Math for Liberal Arts, a college course. Here is the question on my practice quiz: A lottery drawing consists of choosing 6 numbers between 1 and 30 (any order). If you choose 6 numbers between 1 and 30, what is the probability that EXACTLY 4 of the numbers you choose are correct? The answer is 0.00697 I do not know how they derived this answer. I have tried many different ways and can not come up with the answer they got. I tried this: 30 C 4 x 26 C 2 divided by 30 C 6. This way doesn't seem to work, so I must not be on the right track. I have similar problems like this as well. Can you help? I need it right away today, sorry for the rush.```
 ```Hi Arturo, Thanks for your question. I will assume that you are familiar with the combinatorial function since you make use of it in your question. I will follow you in denoting the function with 'C'. Just as a refresher, the combinatorial function works as follows: y C x = y! / (x! * (y-x)!) It's also useful to note that Excel has a combinatorial function. To get 30 C 6 you would type '=combin(30,6)' into a cell. OK, enough of the preliminaries... **Important**: For any lottery type problem in which they ask the probability of matching exactly x numbers after choosing y from a pool of n, the formula will be: (y C x * n-y C y-x) / n C y So in the example you provide, we want the probability for matching exactly 4 numbers after choosing 6 from a pool of 30. The resulting formula is: 6 C 4 * 24 C 2 / 30 C 6 6 C 4 is equal to 15. This means that there are 15 ways of including 4 of the 6 correct numbers. 24 C 2 is equal to 276. This means that there are 276 ways of including 2 of the 24 incorrect numbers. 30 C 6 is equal to 593,775. This means that there are 593,775 ways of arranging the 30 numbers into groups of 6. Finally, (15 * 276) / 593,775 = .00697. So given that there are 15 ways of arranging 4 correct numbers in a draw of 6 and there are 276 ways of arranging two of the incorrect 24, we multiply 15 by 276. This gives us all the possible ways in which we can draw 4 correct numbers and 2 incorrect numbers. We then divide that number by the total number of possible ways of drawing 6 from 30: 593,775. The probability of exactly 4 of the 6 numbers drawn from a pool of 30 being correct is .00697. You might find the following websites helpful: Info on the combinatorial function: http://www.wizardofodds.com/games/pokerodd.html Info on calculating lottery probabilities: http://www.math.mcmaster.ca/fred/Lotto/ More examples: http://www.wizardofodds.com/games/lottery-probability.html If anything is unclear, please request clarification prior to submitting a rating. Best of luck! -Blinkwilliams-ga```
 arturo-ga rated this answer: `Another outstanding job, thank you.`