A restaurant has
7
pizza toppings to choose from. How many different
2
-topping pizzas are possible?
To find the number of different 2-topping pizzas possible, we can use the concept of combinations. A combination is a selection of items without regard to the order in which they are arranged.
In this case, we want to select 2 toppings out of the 7 available. The formula to calculate the number of combinations is given by:
C(n, k) = n! / (k! * (n - k)!)
Here, n represents the total number of available options (in this case, 7 toppings), and k represents the number of choices we want to make (in this case, 2 toppings).
Applying the formula:
C(7, 2) = 7! / (2! * (7 - 2)!)
Simplifying:
C(7, 2) = 7! / (2! * 5!)
Calculating the factorials:
C(7, 2) = (7 * 6 * 5!) / (2! * 5!)
Simplifying further:
C(7, 2) = (7 * 6) / 2!
Now calculating the factorial of 2:
2! = 2 * 1 = 2
Substituting the values:
C(7, 2) = (7 * 6) / 2
Calculating:
C(7, 2) = 42 / 2
C(7, 2) = 21
Therefore, there are 21 different 2-topping pizzas possible from the given 7 toppings.
To find the number of different 2-topping pizzas, you can use the concept of combinations.
The formula to calculate the number of combinations is given by:
n C r = n! / (r! * (n-r)!)
Where n is the total number of options available (in this case, the number of pizza toppings) and r is the number of choices we need to make (in this case, 2 toppings).
Using the given information:
n = 7 (the number of pizza toppings)
r = 2 (the number of choices we need to make)
We can substitute these values into the formula:
7 C 2 = 7! / (2! * (7-2)!)
Calculating the factorial terms:
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
2! = 2 * 1 = 2
(7-2)! = 5!
Substituting the factorial terms into the formula:
7 C 2 = 5040 / (2 * 120)
Calculating the denominator:
2 * 120 = 240
Substituting the denominator into the formula:
7 C 2 = 5040 / 240
Calculating the final result:
7 C 2 = 21
Therefore, there are 21 different 2-topping pizzas possible.