#### dial911book

##### New member

- Joined
- Jun 17, 2019

- Messages
- 4

Now -- another person starts dealing out one card at a time from a shuffled 52 card deck. The first card is, say, 5C. Oops - 5C is not the correct first card in my predefined sequence. So she puts the card back in the deck, shuffles, and deals out a 2C. Fine, that matches the predefined sequence. She deals at random the next card. Oops, it is a 10S. So she

*takes both of the cards back into the deck, shuffles, and starts over.*Question: How many of these deals, where there is no guarantee that the first or second or third … or 51st card, will be the correct one in the sequence -- and

*-- would be expected to occur (on average) to obtain all 52 card dealt out in the specified order without a reshuffling?*

**whenever the wrong card comes into the sequence she is dealing, she takes all of the cards back, shuffles, and starts again**(If you can show how you made the calculation, that will greatly help me, so I can generalize to other related sorts of problems.)

(If it is simpler to show how it is done for, say, 5 distinct cards, that's fine, if I can generalize the formula )

(It occurs to me that the solution is a number much larger than 52!, which is the number of discrete arrangements of all 52 cards. I just don't know how to think about the problem of restarting from scratch when the sequence is part way but then fails.)

-Richard