According to the recent Pizza Hut
commercial starring Jessica Simpson,
how many combinations of toppings
are possible on the new 4 for All pizza ?
+++++++++++++++
06-13-04, 05:46 PM
methos
The number she gives is 6,321,000, but I think she is wrong...

06-13-04, 05:57 PM
methos
Assuming each pizza needs exactly 4 toppings out of the 18 possible toppings, and none of these toppings can be repeated on the same pizza, the total number of combinations for one pizza is:
18C4 = 18!/[(18-4)!*4!] = 3060

The same equation holds for determining the total with all 4 pizzas
3060C4 = 3060!/[(3060-4)!*4!] = 3,646,049,676,885

If you allow for the same topping to be used more than once, for two or more identical pizzas, or for less than 4 toppings on one or more of the pizzas, the number of possibilities gets even larger.

My probabilty is shakey, but I think that's right.


On edit: I now see that this is exactly what SailRacer said, only without rounding the final number.

06-13-04, 06:11 PM
dogspit
6,321,000 is indeed the answer I was looking
for ! I think this would make an interesting
thread in the math forum ! Thanks everyone
for all the answers !!!!!

06-13-04, 09:39 PM
MommyTimesTwo
Okay, what did I do wrong?? I'd really like to know how to figure this kind of problem out properly. (and for the record, I'm a brunette Big Grin)

06-13-04, 10:04 PM
methos
Mx2 -

for your first pizza
18 choices for the first topping
17 for the second
16 for the third
15 for the fourth
As you calculated, this is 18*17*16*15 possibilities.
[18!/(18-4)!] = 18*17*16*15

BUT, this would count, say, mushroom, pepper, onion, ham as a different pizza than ham, onion, pepper, and mushroom. To correct for this, you divide by the factorial of the number of toppings (hence the 4!) to get the number of unique combinations.

Then, you do the same with the 3060 choices each for four pizza as you did with the 18 choices for four toppings.

There are other possibile 'rules' of what can go on the pizzas (say, letting the same topping be used twice on the same pizza), but since the rules weren't spelled out for us in the commercial and since all other reasonable rules would result in even more possiblities, I chose to leave it at that.

06-13-04, 11:45 PM
MommyTimesTwo
Okay, I get that--that totally makes sense. Thank you for explaining it! Smile

06-14-04, 10:03 AM
methos

quote:Originally posted by dogspit:
I think this would make an interesting
thread in the math forum !



Indeed. I've posted a question in two parts.
(1) Checking to see if my & SR's math is correct.
(2) determining the number of possibilities in the case where toppings can be repeated on the same pizza and/or entire pizzas can be repeated

06-16-04, 10:06 AM
Texan-In-Exile
Dawg - I was really expecting the answer to be 6,666,666!

This message has been edited. Last edited by: DorianGreyed,