Dear Ken Selby, Chairman, Mazzio’s Italian Eatery:

Tonight, my family and I ate pizzas from Mazzio’s. They were very tasty. ‘Delicious’ is not too strong a word (and I say this as one not prone to hyperbole). But affixed to the pizza boxes was an advertisement for your new “Mia Pasta” campaign, the text of which contained a deceptive falsehood.

Start with one of three pastas, then choose one of six sauces and one of four meats, plus three of eleven veggies.

With so many options, your possibilites are endless!

(emphasis in original)

Endless? That would seem to be a surefire enticement to purchase your meal. “I can’t go wrong,” the prospective diner would think, “since my possibilities are endless!” But I’m afraid your claim of infinity is demonstrably false. Taking the choices (as you have described them yourself), we may calculate the possible allowed combinations thusly:

3 x 6 x 4 x 11! / (3! x (11-3)!)

The unassailable science of mathematics yields a total number of only 11,880 “Mia Pasta” possibilities, and 11,880, being a finite number, is manifestly not infinite. QED.

You may wish to claim a right of poetic (or some such) license, and assert that 11,880, while not technically infinite, is such a high number that it is virtually infinite. Such a claim could be readily dismissed by imagining, say, an $11,880 federal budget, or an ocean filled with 11,880 gallons of water. Far from being infinite, or even virtually so, 11,880 is a triflingly small number. A pittance. But the unwary pastaphagous patrons of your establishment are nowhere advised that their choices are subject to such a severe limit, nor indeed any limit!

Fortunately, redressing this problem presents no difficulty. Here are some suggestions for the reworded advertising copy:

• “With so many options, your possibilities are more than if there were fewer options!”
   
• “With so many options, your possibilities are 3 x 6 x 4 x 11! / (3! x (11-3)!)”
   
• “With so many options, your possibilities are exactly 11,880.”
   
• “With so many options, your possibilities are exactly 11,880! Note the exclamation point following 11,880 in the foregoing sentence is for emphasis, and not for factorialization!”
   
• “With so many options, your possibilities are endless, or 11,880, whichever is lower!”
   
• “With so many options, your possibilities are actually 106,920, since we forgot to mention we offer nine different beverages!”

I look forward to seeing your corrected flyers, and many more delicious Mazzio’s meals in the future.

Best regards:

Sean Gleeson
sean@gleeson.us
http://sean.gleeson.us/

UPDATE: The error has been corrected! Please read Mazzio’s makes good!