In how many ways can 5 identical apples be put into 3 different bowls

(*Disclaimer: not necessarily the right answer, just my attempt)

In order for all baskets to have at least 1 apple, you can have two types of distributions:
i) 3 - 1 - 1 (Can happen 3x different ways since the baskets are different)
ii) 2 - 2 -1 (Can also happen 3x different ways since the baskets are different)

I learned something through this exercise! Since the apples are identical - There will only be 1 way of choosing them. Therefore the first basket has 1 way of choosing 3 apples (not 5C3). Therefore the number of ways to choose apples so that each basket has at least 1 will be:

i) (1x1x1) x 3
+
ii) (1x1x1) x3 = 6 ways

Answer is A

Bunuel - is this correct?