There are 15 available toppings and 5 different pizza sizes in a pizza restaurant. If Maria wants to order a 4-topping pizza, how many different pizzas could she order?
My solution: 15C4/5!
4 topping 15C4=1365 Is this correct?
Thank you.
Your solution is almost correct. However, since there are 5 different pizza sizes, you need to multiply the number of possible combinations of toppings by 5 as well.
So the correct solution is:
Number of 4-topping pizzas = (15 choose 4) * 5
Using the formula for combinations, which is nCr = n! / (r!(n - r)!), we have:
Number of 4-topping pizzas = 15! / (4!(15 - 4)!) * 5
Simplifying the equation:
Number of 4-topping pizzas = (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1) * 5
Number of 4-topping pizzas = 1365 * 5
Number of 4-topping pizzas = 6825
So Maria could order 6825 different pizzas with 4 toppings each.
To calculate the number of different pizzas Maria could order with 4 toppings, you can use the combination formula. The formula for combinations is "n choose r", represented as nCr, where n is the total number of options and r is the number of choices.
In this case, there are 15 available toppings, and Maria wants to select 4 toppings for her pizza. So the calculation would be 15C4.
The formula for combination is:
nCr = n! / (r!(n-r)!)
where "!" denotes factorial (e.g., 4! = 4 * 3 * 2 * 1).
For 15C4, the calculation would be:
15! / (4! * (15-4)!)
= 15! / (4! * 11!)
Now let's break down the calculation step by step:
1. Calculate the factorial of 15:
15! = 15 * 14 * 13 * 12 * 11! = 1,307,674,368,000.
2. Calculate the factorial of 4:
4! = 4 * 3 * 2 * 1 = 24.
3. Calculate the factorial of (15 - 4) = 11:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800.
Now, substitute these values back into the original equation:
15C4 = 1,307,674,368,000 / (24 * 39,916,800)
= 1365
So, the correct answer is indeed 1365 different pizzas that Maria could order with 4 toppings.
Hope this helps!