Which precise pita is best for you when there are so many variations and customizations to choose from?  (After all, your appetite and tastes change from day to day, moment to moment, so you need lots of options.)

The Pita Problem Contest: Tell us how many different customized pita choices you have at the Athens Pita Pit and your office may win a Free Catering Platter ($50 Value) from The Pita Pit.

Be the hero of your office. Do a little math (or just guess if you like).   Earliest e-mailed  entry with the correct (or closest) answer wins.

Just one one entry per e-mail address (so give it your best shot.)

1.  First, the Pita Pita offers 28 BASIC PITAS (Chicken Caesar, Hummus, B.L.T., Philly Steak, etc., etc.)  So there are 28 choices right there.

But then... you can start customizing each of the 28 pitas... (Here's where the fun begins.)

2.  You may choose either a white flour or wheat flour pita.

3.  Then... you may choose to add to your pita any combination of UP TO 17 total different TOPPINGS (lettuce, tomatoes, onions, olives, pineapple, etc. etc.) (Yes, you may have all 17 if you like.) 

4.  Then... you may choose to add UP TO 4 different CHEESES to your pita.

5.  Finally... you may choose to add from zero UP TO TWO DRESSINGS (from the 16 different choices of dressing available: Ranch, Secret Sauce, etc.)

(NOTE: in real life,  you could ask to have as many as all 16 dressings on your pita, but for the purposes of this contest, we've limited it to none, or one, or two dressings, simply because that's the most that most people ever choose.)

OK.  So, based on all those choices, how many possible different customized pitas can you choose to build?  Can you figure it out? (Or guess?)

Your Answer... ?  

(After you've worked on it, see the answer below.)

FIRST... the WINNER  of the CONTEST:

Michelle Cano of the OU Planning and Implementation Office at The Ridges came up with the exact, correct answer. A wild guess? Probably not.

THE CORRECT ANSWER: 16,089,350,144 different pita combinations

HERE'S HOW IT WAS CALCULATED:

The official answer and the explanation below were kindly provided by Chris Holston in the OU Math Department. (Thanks, Chris)

CHRIS HOLSTON's EXPLANATION:

First of all, we need to count up the number of ways for each of the 5
categories and multiply them together.
Let me hint at the reason for this by example. Say you're counting just
base pita and bread type. Well for each choice of bread there is 28 pita
types, so the number counting just those two categories would be 28+28 = 2* 28, and if there were 3 bread types it'd be 3 * 28, etc.

So now we have to count each of the categories.
Obviously 28 for pitas and 2 for breads.

On to toppings (veggies and such). For each individual topping, there are 2 possibilities, you either get it, or you don't. There are 17 total, so
you'd be multiplying 2, 17 times in all (i.e 2^(17)=131072).

By the same line of logic the total in the cheese category is 2^4=16.

The last one will be trickier to explain. If you allowed for anywhere from 0-16 sauces this number would be 2^(16) by the same logic as before, which will add about 3 digits to your total. But under the presumption of only 0-2 sauces we will have to treat each case separately. (In a probability
textbook, these terms are called combinations, or chooses).
Note that there's only 1 way to have no sauce on your pita (16 choose 0 = 1) and 16 ways to pick one sauce (16 choose 1 = 16)
To see the number of ways to pick two sauces, first pick one sauce (16
ways), then pick another (15 left to choose from). The only problem is we counted every possible way twice (i.e. choose hot sauce then mild sauce and choose mild sauce then hot sauce). So we must divide by 2.
(16*15)/2=120 (16 choose 2 = 120).
[For more than 2 sauces it would be a little more complicated to explain
the choose formula.]
Anyway under your given assumptions that makes 1+16+120=137 ways for sauces.
Then as mentioned before we take
28*2*131072*16*137=16,089,350,144.

Thanks to all those who entered the contest.