Final answer:
There are 792 ways to divide twelve pieces of fruit into two baskets containing five and seven pieces of fruit respectively, using combinations.
Step-by-step explanation:
The question asks in how many ways can twelve pieces of fruit be divided into two baskets containing five and seven pieces of fruit respectively. To solve this, we will use combinations. Since the order in which we choose the fruit does not matter, we are dealing with combinations rather than permutations.
We have a total of 12 fruits, and we want to put 5 in one basket and 7 in the other. This can be viewed as simply choosing 5 fruits out of 12 for the first basket, and the remaining 7 will go into the second basket. The number of ways to choose 5 fruits out of 12 is given by 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.
Using the formula, we get C(12, 5) = 12! / (5!7!). Calculating this value, we find that there are 792 possible ways to distribute the fruit.
Thus, the answer to the question is 792, which corresponds to option C.
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