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

The screwengineer Pelle has a box with 16 black screws and 16 white screws.

a. In how many ways can he pick an even(at least 2) amount of screws from the box?

b. Pelle randomly chooses one of the alternatives in (a), what's the chance that gets as many white as black screws?

It is allowed to answer in binomial coefficients.

2. Relevant equations

3. The attempt at a solution

a) easy, sum k from 2 to 32, 32 nCr k => 4294967263 ways.

b) this is the hard part. I have the solution but I don't understand it.

The nbr of nomempty sets with as many black as white screws are (16 nCr 1)^2+(16 nCr 2)^2+...+(16 nCr 16)^2

Divide that by the answer in (a) to get the answer to (b) => 0.28 = 28%

I don't get the part with nonempty sets.

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# Combinatorics - box of white and black screws

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