When items are of different kind (as in your question)
1) 10 different items , 3 different persons(a,b,c)
if there is no extra condition like , A must have K books like-like then adopt following method
B1 : book one has 3 ways to deliver , either to a or b or c = 3 ways
B2 : 3 ways , either to a or b or c...
B3 : 3 ways...
so B1 to B10 every book can be deliver in 3 ways so total ways 3*3*3*3...10 times =310
Now let suppose we have condition like A must have one book at least , so in that case first give 'a' that book , one book out of 10 can be selected in 10 ways (10C1), now remaining 9 books follow the above approach
so total ways = 10*39
Here every one must have atleast 3 books
for a it's 10C3 ways then remaining 7 give b any 3 (7C3 ways) remaining 4 give c any 3(4C3 ways) so remaining 1 can be deliver to anyone => 3 ways
total =10C3 * 7C3 * 4C3 * 3 ways
When items are identical kinds
10 same kinds of items , among 3 persons
Case 1 ) a+b+c=10 ; a>=1 , b>=0 , c>=0
case 2 ) a+b+c=10 ; a,b,c>=0
case 3) a+b+c=10 ; a,b,c>=3
you can follow below link to know how to solve this kind of equations...
https://gateoverflow.in/158719/number-of-solutions#a158731