A draw contains an unsorted collection of black, navy, white, and brown coloured socks. If socks are taken at random, one at a time, what is the minimum number which must be taken to be certain of finding five matching pairs?

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OpenStudy (anonymous):

Can you obtain a formula to find the minimum number of socks which must be taken to be certain of finding p matching pairs when the draw contains an unsorted collection of c different coloured socks?

OpenStudy (anonymous):

This is just a small challenge problem if you wish to think about it.

OpenStudy (anonymous):

17

OpenStudy (anonymous):

No

OpenStudy (anonymous):

sure?

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OpenStudy (anonymous):

Yes :-)

OpenStudy (anonymous):

how?

OpenStudy (anonymous):

You can think about it as an induction so step by step.
If you take 5 socks out than surely there must be 1 matching.
If we take 2 more than again there will be 1 matching for sure.
So to get 5 matching we need 3+2*5

OpenStudy (anonymous):

This helps making a formula as well

OpenStudy (anonymous):

oh, I read the question wrong. I thought you meant five gloves of the same color. fail.

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OpenStudy (anonymous):

I see, but you can see now that it is not gloves but socks :DD