Factorial problem

Joined
Apr 12, 2014
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1
Hi and thanks in advance for any help you can provide.

I have a tarot decek of 78 cards.

After shuffling the deck is completely random.

I lay down the cards in ten positions and record the answers.

I shuffle again and they are completely random.

I put down ten cards again. 7 of the 78 cards reappear. Of these, 5 are in the exact same position as the first deal.

I shuffle them again and they are completely random.

I put down ten cards again and 8 of the same 10 cards from the first deal of10 reappear. Of these, 7 are in the exact same position as from the first deal.

What are the odds of this happening, and how do I figure this out? I'm at a loss...

Thanks so much for any help,

An American in Copenhagen
 
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