how many ways can you choose 3 flavors of yogurt out of five flavors of yogurt
5C3 = 5C2 = 5*4 / 1*2 = 10
Or, if the order is important,
5P3 = 5*4*3 = 60
In how many ways can you choose 5 flavors of yogurt and 5 topping?
To calculate the number of ways to choose 3 flavors of yogurt out of 5, we can use the concept of combinations. In mathematics, combinations refer to the selection of items from a larger set without considering the order. The formula for combinations is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to be selected.
In this case, we have 5 flavors of yogurt and we want to select 3 flavors. Plugging these values into the formula:
nCr = 5! / (3!(5-3)!)
= 5! / (3! × 2!)
To simplify further, we calculate the factorials:
5! = 5 × 4 × 3 × 2 × 1 = 120
3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
Now substituting these values into the formula:
nCr = 120 / (6 × 2)
= 120 / 12
= 10
Therefore, there are 10 different ways to choose 3 flavors of yogurt out of 5 flavors.