Average number of $5$-card draws before all $52$ cards in a deck are drawn. So an interesting question was brought to me today and I'm not sure how to formulate the equation to answer it. A person draws $5$ cards from a deck, writes the cards down, puts the cards back in the deck and reshuffles. What is the average number of draws they have to perform before all $52$ cards are drawn?

What about before before $45$ out of the $52$ cards are drawn?

Finally, how many draws if red cards were twice as likely to be drawn as black cards?

If you could show the equation for each it would be much appreciated.
This sounds like the coupon collector problem.
https://en.wikipedia.org/wiki/Coupon_collector%27s_problem

While the 5 card draw does make it easier, for a single card hand it will take 236 draws on average to collect all 52 cards.

So as an upper bound for the 5 card version I would say 48 hands.
This sounds like the coupon collector problem.
https://en.wikipedia.org/wiki/Coupon_collector%27s_problem

While the 5 card draw does make it easier, for a single card hand it will take 236 draws on average to collect all 52 cards.

So as an upper bound for the 5 card version I would say 48 hands.