In how many ways 12 apples can be distributed among 4 people?  Ops:   A. 469    B. 457    C. 455    D. 488

This problem can be solved using the concept of combinations with repetition in combinatorics.

The formula for combinations with repetition is: C(n + r - 1, r), where n is the number of items to choose from (in this case, apples), and r is the number of items to choose (in this case, people).

Step 1: Identify n and r. Here, n = 12 (apples) and r = 4 (people).

Step 2: Plug n and r into the formula. C(12 + 4 - 1, 4) = C(15, 4)

Step 3: Calculate the combination. C(15, 4) = 15! / [4!(15-4)!] = 1365

So, there are 1365 ways to distribute 12 apples among 4 people.

However, none of the options (A. 469, B. 457, C. 455, D. 488) match this answer. There might be a mistake in the question or the provided options.