Question

In how many ways can twelve pieces of fruit be divided into two baskets containing five and seven pieces of fruit, respectively?

A) 12
B) 66
C) 252
D) 924

Answer 1

There are 792 ways to divide twelve pieces of fruit into two baskets with five and seven pieces of fruit, based on the combination formula. Since the options provided do not match this answer, the question might contain an error or require a different interpretation.

Step-by-step explanation:

The question is asking in how many ways twelve pieces of fruit can be divided into two baskets containing five and seven pieces of fruit, respectively. This is a combinatorial problem where we need to calculate the number of combinations.

For the first basket, we choose 5 pieces of fruit from 12, which can be calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items, and k is the number of items to choose.

So, we calculate C(12, 5) for the first basket. The seven remaining pieces automatically go into the second basket, so we do not need further calculations for the second basket. Using the combination formula, we get C(12, 5) = 12! / (5! * (12 - 5)!) = 792.

Therefore, there are 792 ways to divide twelve pieces of fruit into two baskets containing five and seven pieces of fruit, respectively.

However, the provided options do not include 792, so the question likely contains an error or is looking for a different interpretation.