SOLUTION: 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

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

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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