Distribute the fruits!
Find the number of ways in which apples, bananas and oranges can be divided into persons so that each person may get fruits.
Note: Assume all fruits of one kind are identical.
The answer is 331.
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1 solution
Let 2 persons are A and B , and A get x apples, y bananas , z oranges .
Then, x+y+z=30 ( 0 ≤ x, y, z ≤ 20 )
the number of (x,y,z) is 3H30 - 3× (3H9 = 55 ) =331
(∵ if 21≤x , (x-21)+y+z=9 : 3H9 )