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aqgarcia · Jul 11, 2007, 11:10 AM

Suppose I have 3 music CDs. Each CD has 18 individual music tracks (unique). What are the odds or probability for the following:

Given: 2 People -- they are to Pick 1 track from each CD.

Odds / Probability (between the two people): 0 matches, 1 matches, 2 matches and 3 matches ?

thanks - :)

galactus · Jul 12, 2007, 05:15 PM

The probability there are 3 matches is $\left(\frac{1}{18}\right)^{3}$

Can you figure out the others? If not, let me know.

aqgarcia · Jul 12, 2007, 05:22 PM

Sorry - I don't know the other permutations -- 0 match, 1, and 2... thanks for your answers

galactus · Jul 12, 2007, 05:28 PM

Well, let's see, think a little about it.

The probability there are 2 matches would be:

$\underbrace{(\frac{1}{18})^{2}}_{\text{2 matches}}\overbrace{(\frac{17}{18})}^{\text{no match}}=\frac{17}{5832}$

The probability there is a no match is 17/18, because the other person chose everything but the one the other chose. See? So, what if there are 3 no matches?

BTW, these aren't permutations. Order is not an issue.