Distributing fruits to 3 people.

Question

We have 8 (identical) apples, 6 oranges, and 7 pears, to distribute among 3 people

A) without restriction

B) where each person gets at least 1 pear.

For A, I had tried to use "stars and bars" and got $10\choose 2$$ 9\choose 2$$8\choose 2$.

Then for B, I calculated how many ways to distribute them where each person gets exactly 0 pears, and then subtracted that from the total, getting $10 \choose 2$ [$9\choose 2$$-1$]

Answer 1

Your attempt of A) is indeed correct. The second question can easily be answered by first giving everyone a pear and then dividing the ones left over. Do you think you can answer it now?

Answer 2

A looks good

For B, just give everyone 1 pear first. So instead of 7 pears, there are now only 4 pairs. Then do it the same way you did A.