Question

How many ways are there to select four pieces of fruit from a bowl containing apples, oranges, and pears if the order in which the pieces are selected does not matter, only the type of fruit and not the individual piece matters, and there are at least four pieces of each type of fruit in the bowl?

Answer 1

To find the number of ways to select four pieces of fruit from a bowl containing apples, oranges, and pears, we use the combinations with repetition formula. There are 3 types of fruit, and we want to select 4 pieces, yielding 15 different ways to make the selection.

Step-by-step explanation:

The student's problem involves counting the number of ways to select four pieces of fruit from a bowl containing at least four pieces of apples, oranges, and pears, with the order of selection not mattering. This is a combinatorial problem that can be solved using the concept of combinations in mathematics.

Since there is a large enough quantity of each fruit, we can treat this as a problem of combinations with repetition. We use the formula (n+k-1)! / (k!(n-1)!) where n is the number of fruit types (which is 3: apples, oranges, and pears) and k is the number of fruits selected (which is 4). So the problem is equivalent to finding combinations of n = 3 objects taken k = 4 at a time with repetition.

Using the formula, we calculate: (3+4-1)! / (4!(3-1)!) = 6! / (4!2!) = (6*5) / (2*1) = 15. Therefore, there are 15 different ways to choose four pieces of fruit from the bowl.

Answer 2

The number of ways to select four pieces of fruit from a bowl containing apples, oranges, and pears is 1/4.

Step-by-step explanation:

The number of ways to select four pieces of fruit from a bowl containing apples, oranges, and pears can be found using combinations. Since the order doesn't matter and only the type of fruit matters, we can use the concept of combinations. The formula for combinations is nCr, where n is the total number of fruits and r is the number of fruits we want to select. In this case, we have 3 types of fruits (apples, oranges, and pears) and we want to select 4 fruits. So the number of combinations is 3C4, which is equal to 3! / (4!(3-4)!). Plugging in the values, we get 3C4 = 3! / (4!(3-4)!) = 3! / (4!(-1)!) = 3! / 4! = (3*2*1) / (4*3*2*1) = 6 / 24 = 1/4.