(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Basically the garbage information summed up: a truck is transporting a bunch of batteries, with lots of different brands. The truck crashes and the batteries and scrambled.

Suppose the number of pairs of batteries isn. Each pair is a different brand. If 2rbatteries are chosen at random, and 2r<n, show that the probability there is no matching pair, by brand, is:

2[tex]^{}2r[/tex] n! (2n - 2r)! / (2n)! (n - 2r)!

2. Relevant equations

I don't know, but I can see that the expectation formula E(x) = [tex]\Sigma[/tex] (x P(X=x)) and the Permutation formula nPr = n! / (n - r)! and Combination formula nCr = n! / (n - r)! r! may be useful as they seem to be of a similiar format to the given equation.

3. The attempt at a solution

The part is struggle most with is why they have taken 2 to the power of 2r. (2n - 2r) is obviously total batteries less chosen batteries. The denominator is total batteries by pairs less batteries, but again I'm at a loss as to why they have done this.

Can anyone shed some light?

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# Homework Help: Statistics (probability) problem

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