sampling without replacement - confusing probability question!!

I've been going in circles trying to work out the solution to this problem:

Suppose that 10 cards, of which 7 are red and 3 are green, are put at random into 10 envelopes, of which 7 are red and 3 are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contains a card with a matching colour (k= 1,2,......,10)

By intuition I realise k cannot be less than 4 but then I get confused.

Any help would be appreciated!

Re: sampling without replacement - confusing probability question!!

Is the problem allowing you to choose "k", or does it want the maximum or minimum value? Because it is asking two questions: the probability and the value of k.

Re: sampling without replacement - confusing probability question!!

The questions gives us that the value of k goes from 0 through to 10... I interpreted the question to be asking for the probabilities of each if these events ie prob of 10 matching pairs, 9 matching pairs etc.

I'm having trouble determining these probabilities, I'm not sure how to count the outcomes for the respective events and without that I can't determine the probabilities, can I?

The only thing I know Is that there cannot be less than 4 matching pairs because even if all three green cards go into red envelopes and then three red cards go into green envelopes 4 pairs of red cards and red envelopes remain...

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Re: sampling without replacement - confusing probability question!!

Re: sampling without replacement - confusing probability question!!

Thank You so much highvoltage!

I knew the solution was going to be quite simple but I over thought it by trying to determine counting methods :S