Question

there are fifteen different snacks to choose from in a vending machine. you pick three snacks. how different ways can you choose your three snacks?

Answer 1

There are 455 different ways to choose three snacks from fifteen different options in a vending machine, calculated using the combinations formula C(n, k) = n! / (k! * (n-k)!).

Step-by-step explanation:

To determine how many different ways you can choose three snacks from fifteen available in a vending machine, we can use the concept of combinations in mathematics. The formula for combinations is given by C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' is the factorial of a number. In this case, n = 15 and k = 3.

Calculating the combinations, we get:

1. 15! = 15 × 14 × 13 × ... × 1
2. 3! = 3 × 2 × 1
3. (15-3)! = 12!
4. C(15,3) = 15! / (3! × 12!) = (15 × 14 × 13) / (3 × 2 × 1)
5. C(15,3) = 455

Therefore, there are 455 different ways to choose three snacks from the fifteen available.