How many combinations of hamburgers can you have with 12 toppings?
depends - how many toppings per burger?
If any possible combination of toppings is allowed, you basically have
C(12,0) + C(12,1) + ... + C(12,12) = 2^12 = 4096
4095 if you don't allow 0 toppings.
To find the number of combinations of hamburgers with 12 toppings, we can use the concept of combinations in combinatorics.
Each topping can be classified as either included or not included on a particular hamburger. For each topping, there are two possibilities: it can be included (1) or not included (0).
Since we have 12 toppings, we can think of creating a 12-digit binary number, where each digit represents a topping. For example, the binary number 101010101010 would indicate that the burger includes the 1st, 3rd, 5th, 7th, 9th, and 11th toppings.
To find the number of different combinations, we need to calculate the total number of possible binary numbers we can create using 12 digits.
Since each digit has two possibilities (either 0 or 1), the total number of combinations can be found by raising 2 to the power of the number of digits. In this case, it would be 2^12.
Calculating 2^12, we find that there are 4,096 possible combinations of hamburgers with 12 toppings. Hence, you can have 4,096 different combinations of hamburgers with the given 12 toppings.