1. ## Finding Probabilities

I'm taking a Mathematical Statistics class, and the first chapter is on probability. Most of it makes sense, but I'm still trying to understand how to tackle certain problems (when to use permutations over combinations, etc.)

Here is one problem (out of several) that I'm having trouble trying to set up:

In a state lottery four digits are drawn at random one at a time with replacement 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

Source: Probability and Statistical Inference, 7e by Hogg and Tanis. Problem 1.3-7

I'm pretty sure that the number of possible 4-digit combinations is $10^4=10,000$, but I'm not sure where to go from there.

I'd appreciate any help!

--Chris

2. Originally Posted by Chris L T521
I'm taking a Mathematical Statistics class, and the first chapter is on probability. Most of it makes sense, but I'm still trying to understand how to tackle certain problems (when to use permutations over combinations, etc.)

Here is one problem (out of several) that I'm having trouble trying to set up:

Source: Probability and Statistical Inference, 7e by Hogg and Tanis. Problem 1.3-7

I'm pretty sure that the number of possible 4-digit combinations is $10^4=10,000$, but I'm not sure where to go from there.

I'd appreciate any help!

--Chris
Think of the possibilities as representing 4-digit numbers from 0000 to 9999; as you said, there are 10,000 of them.

For (a), ask yourself how many 4-digit numbers can be created using each of the digits 6,7,8,9 exactly once. Then divide by 10,000 to find the probability.

The remaining problems are similar.

### in a state lottery four digits are drawn at random one at a time

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