How many ways can you choose 2 toppings from 5 available toppings for a pizza?

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Question: How many ways can you choose 2 toppings from 5 available toppings for a pizza?

Options:

Correct Answer: 10

Solution:

The number of ways to choose 2 toppings from 5 is C(5, 2) = 10.

How many ways can you choose 2 toppings from 5 available toppings for a pizza?

How many ways can you choose 2 toppings from 5 available toppings for a pizza?

Step 1: Understand that you have 5 different toppings to choose from.
Step 2: You want to select 2 toppings from these 5 toppings.
Step 3: Recognize that the order in which you choose the toppings does not matter (choosing pepperoni and mushrooms is the same as choosing mushrooms and pepperoni).
Step 4: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items (5 toppings) and r is the number of items to choose (2 toppings).
Step 5: Plug in the values: C(5, 2) = 5! / (2! * (5 - 2)!)
Step 6: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
Step 7: Calculate 2! = 2 × 1 = 2.
Step 8: Calculate (5 - 2)! = 3! = 3 × 2 × 1 = 6.
Step 9: Substitute these values into the formula: C(5, 2) = 120 / (2 * 6).
Step 10: Simplify: C(5, 2) = 120 / 12 = 10.
Step 11: Conclude that there are 10 different ways to choose 2 toppings from 5.

Combinations – This problem tests the understanding of combinations, specifically how to select a subset of items from a larger set without regard to the order of selection.