I just spent the weekend with my friend who owns a Pizza business. He currently offers 20 toppings for his pizzas and we wondered if there was a formula we could plug in the number of toppings and get the right answer out. All of the permutations or combination calculators I have tried so far seem to be off. These are the specific rules: -
The pizza can have anything from 1 to n toppings. No topping or combination of toppings can be duplicated - e.g. you can’t have 5 lots of pepperoni! The order is not important so Topping A, B, C is the same as C, B, A so is not allowed.
We looked at 5 toppings and we think the answer for 5 is 28. If we label each topping A, B ,C ,D ,E the combinations we allow for our rules are: -
A
B
C
D
E
Ab
Ac
Ad
Ae
Bc
Bd
Be
Cd
Ce
De
ABC
Abd
Abe
Acd
Ace
Ade
Bcd
Bce
Cde
Abcd
Abce
Bcde
Abcde
I cannot find an online calculator where I put in 5 and get 28 back. What am I missing? Any help you can offer may allow me to find out the answer to my friends conundrum - the answer to 20 toppings!
The pizza can have anything from 1 to n toppings. No topping or combination of toppings can be duplicated - e.g. you can’t have 5 lots of pepperoni! The order is not important so Topping A, B, C is the same as C, B, A so is not allowed.
We looked at 5 toppings and we think the answer for 5 is 28. If we label each topping A, B ,C ,D ,E the combinations we allow for our rules are: -
A
B
C
D
E
Ab
Ac
Ad
Ae
Bc
Bd
Be
Cd
Ce
De
ABC
Abd
Abe
Acd
Ace
Ade
Bcd
Bce
Cde
Abcd
Abce
Bcde
Abcde
I cannot find an online calculator where I put in 5 and get 28 back. What am I missing? Any help you can offer may allow me to find out the answer to my friends conundrum - the answer to 20 toppings!