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My friends and I are thinking about participating in an event to collect these cards. There are 8 total cards in the set, and we can buy a pack of 10 random cards at a discount. So we were wondering, what is the % chance that we get all 8 of the unique cards in our 10 card pack (assuming each card has an equal chance)? I can't figure out how to calculate it.

kjetil b halvorsen
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Swisse
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  • You count the number of equally probable ways of getting a full set, and divide it by the total number of equally probable ways your $10$ cards might be distributed – Henry Nov 15 '22 at 12:23
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    Please add the [tag:self-study] tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. – kjetil b halvorsen Nov 15 '22 at 13:32
  • This is part of the coupon collector problem. Although the original problem asks for the expectation of how many cards you need until you see all eight of them, some of our threads include formulas for the full distribution, so all you have to do is plug the numbers 8 and 10 into the formulas. – whuber Nov 15 '22 at 16:56

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