Question

Given 8 different toppings to choose from, how many 3-topping pizzas are possible?

Answer 1

Total number of possible 3-topping pizzas are 336 ways.

How do you calculate the number of possible ways something can be arranged?

In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!

Given that,

Total number of items n = 8

number of picking item k = 3

Now,

p(n,k) = $\frac{n!}{(n -k)!}$

p(8,5) =  $\frac{8!}{(8 -3)!}$

         = $\frac{8!}{5!}$

         = $\frac{8.7.6.5! }{5! }$

         = 8 × 7 ×6

p(8,5) = 336 ways

Hence, Total number of possible 3-topping pizzas are 336 ways.

To learn more about  number of Possible ways from the given link:

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Answer 2

Answer:

336 ways

Step-by-step explanation:

Use nPk which is $\frac{n!}{(n-k)!}$. This is $\frac{8!}{5!}$. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.