An Italian food restaurant claims that with the choices of toppings that they offer on their pizzas, you can order about 65,550 different types of pizza. How many toppings do they offer?
for n elements, the number of subsets = 2^n
2^n = 65550
by trial and error
2^10 = 1024
2^15 = 32768
2^16 = 65536
They have 16 toppings
They would be able to make 65536 different kinds, which would include no toppings at all, YUK
and the works, WOW (16 toppings ?)
To find out how many toppings the Italian food restaurant offers, we can use the concept of combinations.
Let's assume the number of toppings they offer is 'n'.
According to the concept of combinations, the number of ways to choose 'r' items from a set of 'n' items is given by the formula: nCr = n! / (r!(n-r)!), where '!' represents factorial.
In this case, we want to find the value of 'n' based on the fact that there are 65,550 different types of pizza when considering all possible combinations of toppings.
Therefore, we can set up the equation:
65,550 = nCr
Using some trial and error, we can find that when n = 12 and r = 5, the combination value is equal to 65,550.
So, the Italian food restaurant offers about 12 different toppings on their pizzas.
To find out how many toppings the Italian food restaurant offers, let's use the concept of combinations.
The formula for combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of options (toppings)
- r is the number of choices (toppings on a pizza)
- ! denotes factorial, which is the product of all positive integers less than or equal to a given number
In this case, we have C(n, r) = 65,550
Now, let's solve for n.
To simplify the calculation, we can try different values of r until we find a suitable number of toppings that gives us 65,550 combinations.
Let's start with r = 1:
C(n, 1) = n! / (1! * (n-1)!) = n! / (n-1)!
Since 1! is equal to 1, we can rewrite the equation as:
C(n, 1) = n
65,550 = n
Hence, the number of toppings offered by the Italian food restaurant is 65,550.