A certain pizza restaurant offers three different sizes of pizza and eight different toppings.
How many distinct pizzas having two different toppings can be made?
======================================
I think part of the answer to the question is
(8)\
(2)/ where I choose 2 toppings from 8.
==> 8!/ (6!* 2!)= 28
But im not sure what to do from there, if it's correct.
ok so far.
Wouldn't those 28 ways also be available in each of the 3 sizes of pizza?
so final number of ways = 3x28 = 84
oh, now wasn't that simple, thank you reiny
Thank you
Yes, you are correct in calculating the number of ways to choose 2 toppings from a total of 8 toppings. However, this is just one part of finding the number of distinct pizzas with two different toppings.
To calculate the total number of distinct pizzas with two different toppings, you need to consider the different pizza sizes. Since the question states that there are three different sizes of pizza, each size can be combined with the 28 different combinations of two toppings.
To calculate the total number of distinct pizzas, you need to multiply the number of different pizza sizes with the number of topping combinations:
Total number of distinct pizzas = Number of pizza sizes × Number of topping combinations
Since there are 3 different sizes and 28 different topping combinations, the total number of distinct pizzas with two different toppings is:
Total number of distinct pizzas = 3 × 28 = 84
Therefore, there can be a total of 84 distinct pizzas with two different toppings at this pizza restaurant.