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what are the total number of non repeating combinations of an unordered list of 54 items?

For example how many different pizza could be made with 54 different toppings, including all 54 on one pie etc, not counting repeats (ie pepperoni & mushroom = mushroom & pepperoni, & only count as 1 unique pizza combo)

Public Comments

1. 54/1 + (54*53)/(2*1) + (54*53*52)/(3*2*1) + ... + 54!/54!
2. a lot
3. 2915
4. 54 to the power 54, alot of pizzas like 12 times 12 is 144 combinations of 12 how about the crust and the pizza sauce does dat count too non repeated combinations can be repeated for as many times at it wishes they are only nonrepeated bc they were first a pizza with cheese only a first step than if I say a pizza with cheese only and ham then I did repeat the first pizza in my second equation so I think 54 if added together is a 9 then 9 flipped like a pizza dough in the air becomes a 6 so my answer is 6 Lapis Lazuli
5. If I interpret the question correctly, you can have any number of items on the pizza (ie, maybe just 1 topping, maybe 54, maybe anywhere in between). If that's so, then the answer is a lot (1.8e16). How do you get this? Imagine you just have one topping. How many possibilities: 54 (any one of the 54). Imagine you have a pizza with 54 toppings. How many possible combinations are there: just 1 (all 54). What about 53 toppings. How many possible combinations: (54-- every scenario of one topping missing). Those are relatively easy. Now imagine you have 2 toppings. How many combinations are there: 53 combinations with pepperoni (it plus any of the others), plus 52 combinations with mushrooms (all but pepperoni, which you've already counted), plus 51 combinations with onions (all but pepperoni & mushrooms, which you've already counted), etc. It turns out there are 1,431 such combinations of two toppings. You can calculate this using a formula called (relatively helpfully) combination. The formula for picking k unordered items from a list of n items is n!/((n-k)! * k!), where ! is "factorial"-- multiplying the positive integer by every positive integer less than it. Eg, 6! = 6*5*4*3*2*1=720. So to pick 2 items out of 54 is 54!/(52!*2!)=1,431. But for your question, you need to add this up for 1 item out of 54, 2 items out of 54, 3 items out of 54... Add it up and you get 1.8e16.