Probability of Winning in State Lottery: 4 Digits

[Hodgey8806]

Homework Statement

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

Homework 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?

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!

 

[lanedance]

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