The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is \_\_\_\_\_\_\_.
Answer: 171
Solutions · 1
Official solution
*(The extracted PDF text for the full working of this item was garbled; the answer 171 does not match the standard surjection formula 320−3⋅220+3 for distinct objects, suggesting the source intends "20 identical oranges" instead --- for identical items, the count would be (219)=171, which matches.)*
For 20 identical oranges distributed to 3 distinct children with each getting at least 1:
\[\binom{20-1}{3-1} = \binom{19}{2} = 171\]