# Give the probability of a permutation of a set of numbers from 0 to 9 if you select:

by Hodgey8806
Tags: combinations, multiplication, permutation, probability, rule
 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!
 HW Helper P: 3,309 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

 Related Discussions Programming & Computer Science 8 Calculus & Beyond Homework 1 Precalculus Mathematics Homework 2 Precalculus Mathematics Homework 13 Precalculus Mathematics Homework 1