Jane has a pizza shop. She has 1 type of crust, 1 type of sauce and 6 toppings. How many 2 topping pizzas can she make. Note the same topping can't be used for 1 pizza
1*1*C(6,2) = 15
extra credit: why did I multiply by 1 -- twice!?
also, proofread before posting. I assume you meant the same topping can't be used twice for 1 pizza.
To find out how many different two-topping pizzas Jane can make, we can use the concept of combinations.
In this scenario, Jane has 6 different toppings, and she needs to select 2 toppings for each pizza. To calculate the number of combinations, we can use the formula:
C(n, r) = n! / (r! * (n-r)!)
Where:
C(n, r) represents the number of combinations of n items taken r at a time
n! is the factorial of n (the product of all positive integers up to n)
r! is the factorial of r
(n-r)! is the factorial of n minus r
Using this formula, we can plug in the values for our scenario:
C(6, 2) = 6! / (2! * (6-2)!)
Calculating this expression:
C(6, 2) = 6! / (2! * 4!)
= (6 * 5 * 4!)/ (2! * 4!)
= (6 * 5) / 2!
= 30 / 2
= 15
Therefore, Jane can make 15 different two-topping pizzas using the given toppings.