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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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Sep4-11, 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 own--I believe lol. Thanks!
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Sep4-11, 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 = 10^4 = 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

now say we chose 8887 there are 4 places the 7 could occur so there probability of winning is

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