# Math Help - Permutations and Probability question...

1. ## Permutations and Probability question...

I don't think I ever learned about this stuff. I'm trying to take some exams for tutoriing job and there is a topic that's in my way though. I get stuck on problems like this:

Say I have 6 blue coins, 8 green coins, and 4 red coins, what is the probability that I will draw at random a blue, then a green, then another blue in that order? ....

So basically from what I've read you can have combinations or permutations, permutations are "orderly" combinations.

Arsenal:

Permutation with repetition where (order matters): $_nP_r=n^r$

Permutation without repetition (order matters): $_nP_r= \frac{n!}{(n-r)!}$

Combination with repetition (order doesn't matter): $_nC_r=\frac{n!}{(n-r)!r!}$

Combination without repetition (order doesn’t matter): $_nC_r=\frac{(n+r-1)!}{r!(n-1)!}$

Where $n$ is the number of things, and $r$ is the number of things being used.

For my case have permuation with repetition and order matters, so is the solution just $\frac{1}{n^r}=\frac{1}{(8+4+6)^3}=\frac{1}{5832}$ ?? that seems a bit off...lol.

Edit Maybe I'm confusing the meaning of "repetition" here. Maybe that does not mean repetition as in the same "type" of coin appearing more than once in a certain permutation, but the repetition of a permutation itself i.e. drawing blue-red-blue could happen more than once.

2. ## Re: Permutations and Probability question...

Say I have 6 blue coins, 8 green coins, and 4 red coins, what is the probability that I will draw at random a blue, then a green, then another blue in that order? ....
So basically from what I've read you can have combinations or permutations, permutations are "orderly" combinations.

Permutation with repetition where (order matters): $_nP_r=n^r$
Permutation without repetition (order matters): $_nP_r= \frac{n!}{(n-r)!}$
Combination with repetition (order doesn't matter): $_nC_r=\frac{n!}{(n-r)!r!}$
Combination without repetition (order doesn’t matter): $_nC_r=\frac{(n+r-1)!}{r!(n-1)!}$
Where $n$ is the number of things, and $r$ is the number of things being used.

Maybe I'm confusing the meaning of "repetition" here. Maybe that does not mean repetition as in the same "type" of coin appearing more than once in a certain permutation, but the repetition of a permutation itself i.e. drawing blue-red-blue could happen more than once.
The important idea here is with or without replacement. Do we keep the coin or put it back.

If it is without replacement and order makes a difference then $\mathcal{P}(BGB)=\frac{6}{18}\cdot\frac{8}{17} \cdot\frac{5}{16}$.

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