To find out how many ways you can choose 3 out of your 12 friends to split the pizza with you, you would use combinations. Combinations are a way to determine how many different groups can be formed from a larger set when the order of selection does not matter. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n - r)!)
Where:
- n is the total number of items to choose from (in your case, n = 12 friends),
- r is the number of items to choose (in your case, r = 3 friends),
- "!" denotes the factorial, which means the product of all positive integers up to that number. For example, 4! = 4 × 3 × 2 × 1 = 24.
Using the formula, let's calculate the number of ways to choose 3 friends out of 12:
C(12, 3) = 12! / (3!(12 - 3)!)
= 12! / (3!9!)
= (12 × 11 × 10 × 9!) / (3 × 2 × 1 × 9!)
= (12 × 11 × 10) / (3 × 2 × 1)
= (12/3) × (11/1) × (10/2)
= 4 × 11 × 5
= 44 × 5
= 220
Thus, there are 220 different ways you can choose 3 out of your 12 friends to split the pizza with you.
