Question 1075839
When drawing cards without replacement from a standard 52 card 
deck find the maximum number of cards you could possibly draw 
and still get the following 

Fewer than 5 hearts<pre>Think of having the deck of cards stacked with 9 of the 13 hearts 
on the bottom of the deck and the other 4 hearts anywhere
among the top 43 cards.

Then if we turn the cards over from the top one at a time, we would
turn over a maximum of 43 cards before we would get the 44th card
to give us 5 hearts. 

Answer: 43

------------------------------ </pre>Fewer than 7 face cards<pre>Think of having the deck of cards stacked with 6 of the 12 face 
cards on the bottom of the deck and the other 6 face cards anywhere
among the top 46 cards.

Then if we turn the cards over from the top one at a time, we would
turn over a maximum of 46 cards before we would get the 47th card
to give us 7 face cards. 

Answer: 46

Edwin</pre>