Final answer:
The number of ways to distribute 12 apples to 5 students is 792. Option C. 792 is the correct answer.
Step-by-step explanation:
To find the number of ways to distribute 12 apples to 5 students, we can use the concept of combinations. Each apple can be given to any of the 5 students independently, so we have 5 choices for the first apple, 5 choices for the second apple, and so on. Since there are 12 apples, we have a total of 5 x 5 x ... x 5 (12 times). This can be calculated as 5^12, which is equal to 244,140,625.
However, we need to account for the fact that the order in which the apples are distributed doesn't matter. So we divide the total number of ways by the number of ways the apples can be arranged, which is 12! (12 factorial). Using the formula for combinations, the number of ways to distribute 12 apples to 5 students is:
C(12, 5) = 12! / (5! * (12-5)!) = 792
Therefore, the correct option is C. 792.