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Give the probability of a permutation of a set of numbers from 0 to 9 if you select: 
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#1
Sep411, 11:58 AM

P: 130

1. The problem statement, all variables and given/known data
In a state lottery, four digits are to be selected from 0 to 9. Suppose that you win if any permutation of your selected integers is drawn. Give the probability of winning if you select: a) 6,7,8,9 b) 6,7,8,8 c) 7,7,8,8 d) 7,8,8,8 2. Relevant equations Now, this is what I don't have. I can easily find the a) by the multiplication rule 4*3*2*1. But the next few don't make sense with any formula I am aware of. I found there probabilities with a tree diagram. Is there a formula to find out what happens if you replace a 9 with a repeated digit? 3. The attempt at a solution a) 4*3*2*1 = 24. The probability is 24/10000. b) Using a tree diagram, I get 12/10000 c) Another tree diagram, I get 6/10000 d) I thought I had a formula saying divide by 2, but it stops when the tree diagram gives a 4/10000 I really just need to be made aware of a relevant equation. If I have that, I can solve this on my ownI believe lol. Thanks! 


#2
Sep411, 10:01 PM

HW Helper
P: 3,307

i think you'll need to consider a counting argument for each case rather than finding a fits all equation
so there are 10.10.10.10 = 10^4 = 10000 possible outcomes for the lottery now say we chose 8888 there is only one distinct arrangement of this number so the probability of winning is 1/10000 now say we chose 8887 there are 4 places the 7 could occur so there probability of winning is 4/10000 


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