How many ways are there to distribute $7$ (identical) apples, $6$ oranges and $7$ pears among $3$ without restrictions?
Here is my solution below, is this the correct method? If not how can I fix it? thanks!
Using stars and bars on each fruit,
Apples,
$\dbinom{7+3-1}{3-1} = \dbinom{9}{2} = 36$
Oranges,
$\dbinom{6+3-1}{3-1} = \dbinom{8}{2} = 28 $
Pears,
$\dbinom{7+3-1}{3-1} = \dbinom{9}{2} = 36$
Then adding these cases together would give the total ways.