:smack:
Well, you could argue that the order of the pizzas is noticeable…
Thanks. I’d just now worked that out using a 3-choice 2-topping pizza. Now I just have to wrap my brain around why it works and I’ll remember it forever.
I love how educational the SDMB is.
“Pork Topping” is basically a bland sausage. It’s pork, with other added things, like spices. I think they called it that to distinguish it from “Italian Sausage”, which is the spicy pork topping. BTW, “Beef Topping” isn’t hamburger. It’s the beef version of Pork Topping.
Close. For three toppings, your method would count pepperoni-onion-olive, for instance, as different from olive-pepperoni-onion. So the correct 3-topping number is 171615/3! = 4080/6 = 680. Similarly, the two-topping choices are 1716/2! = 136. Your values for 1 and 0 toppings are correct, since 1! = 0! = 1. Adding those up, we get 834. If we assume 18 toppings instead of 17, then we get 181716/3! + 1817/2! + 18/1! + 1, or 988, like the other folks have been getting.
daffyduck, the formula using factorials is the simplest way to write down the formula, but it’s not the simplest way to use it, as you notice. You have C = 3060!/4! * 3056! , but to calculate this, you don’t actually need to calculate 3060! or 3056! (both of which, as you note, are beyond the range of a calculator). What you want to first note is that 3060!/3056! is just 306030593058*3057 , which your calculator can handle (albeit in scientific notation). So 3060!/4! * 3056! = 3.646…*10[sup]12[/sup].
Monzy covered this months ago, and The Waffle House too.
Damn! What would I have had to have done to have figured that out on my own?
I tried to work from the other end and deduce what variables they were using given our assumptions about the forumula.
6.3 million combinations with 4 pizzas means that they believe there are roughly 50 combinations for one pizza (6.3 M ^ 1/4).
To get 50 combinations for one pizza, in combinations of zero through three toppings, that assumes there are roughly five toppings to choose from.
Either the just guessed at the figure or we’re all way off in our understanding of the combinations.
Fair enough.
For no toppings, there’s still only one possible combination. For one topping, there are still only 18 possible combinations. That part’s easy.
For two toppings, there are the 153 pizzas from before, plus 18 pizzas with two of the same toppings. That makes 171 possible pizzas with two toppings.
For three toppings, there are the 816 pizzas from before, and 18 pizzas with three identical toppings. There are 18 choices for a double topping, and 17 possible third toppings, so there are 306 pizzas with two of one topping. That makes a total of 1140 pizzas with three toppings.
So the total number of individual pizzas is 1 + 18 + 171 + 1140, or 1330. Four possible pizzas–that’s (1330 * 1329 * 1328 * 1327)/4!, or 129,787,951,580 possible combinations.
Now, what if we allow customers to order less than 4 pizzas?
For no pizzas, there’s one possibility. Do we want to count this? I don’t–it seems unlikely that someone would call in and order no pizza.
For one pizza, there are 1330 possibilities.
For two pizzas, there are (1330 * 1329)/2! possibilities, which is 883,785.
For three pizzas, there are (1330 * 1329 * 1328)/3! possibilities, which is 391,222,160.
So that’s a grand total of 1330 + 883,785 + 391,222,160 + 129,787,951,580 possible orders. If it makes a difference, that sum is equal to 130,180,058,855.
Monzy blew it:
“Each of the four pizzas is allowed up to four toppings, and there are a total of 18 toppings to choose from. Assuming no repeated toppings, there are 18 choose 4, or 3060, possibilities for each individual pizza.”
Each pizza is allowed three topping per the website.
Plus, they calculated the number of pizzas with exactly four toppings. Not quite right.
Ah, now this is entertaining. Here’s Monzy’s complete analysis:
:smack:
For any math whiz who wants to figure it out exactly, here’s the data to do so because I know Pizza Hut policy:
There a 17 possible items
A plain cheese pizza is also a possibility. HOWEVER, extra cheese ISN’T. For cost reasons, Pizza Hut doesn’t allow in such promos “extra cheese” as an item. (Extra cheese can be had, but you’ll have to pay more than this offer is.)
With this promo, there is no “one half this, the other half that” allowed. Basically, this are 4 mini-pizzas at one price, and half items are allowed only on the bigger ones.
Someone can order “double pepperoni, onion”, etc.
Someone can order less than the max 3 allowed. Thus “just onion” is OK. HOWEVER, they can ALSO order “onion, onion, onion”, where they’ll get a pizza laden with onions. Thus, with a pizza with just onions, “onion”, “double onion” and “triple onion” are unique possibilities.
There are also these possibilities:
Cheese Lover’s
Meat Lover’s®
Pepperoni Lover’s®
Sausage Lover’s®
Veggie Lover’s®
Chicken Supreme
Supreme
“Super Supreme” exists, but would not be allowed with this promo. With this last group above, substitutions and deletions are NOT allowed.
My math is a little rusty. However, I can immediately recognize that the possibilities are WAY more than around 6 million.
Considering that she says “According to chance and probability” just before she says the number, I completely tune out after that.
What does it have to do with chance and probability? Absolutely nothing.
They’re trying to confuse people by including incomprehensible math, but combinatorics was too far over their heads?
Dude, it’s the Muppets and Jessica Simpson! How many times have either of them used accurate mathematics?
Well, yeah, I know. That’s why I was surprised that anyone even thought there was a chance the number in the commercial was correct.
Even though he’s only on Sesame Street, the Count is never wrong when it comes to math!
No need to be insulting about it.
I’m sorry, I didn’t mean for it to be insulting.
I just never considered that the number might be correct due to the aforementioned “chance and probability” thing, and the talking frogs, pigs, and other various animals.
It did turn out to be an interesting exercise, though.
heh… Don’t know how she missed that calcuation. Boy, is she dumb.
If Pizza Hut adds Chicken of the Sea as a topping, would that count as two toppings, seeing as how it’s both poultry and fish? What about buffalo wings?
I think some people are discounting some duplicate pizzas. It’s certainly an option for all 4 pizzas to be pepperoni/g. pepper/cheese. What we need to eliminate is counting both pepperoni/g. pepper/cheese AND cheese/pepperoni/g. pepper on Pizza 1.