SOLUTION: A dart board has 4 concentric circles, the inner circle has the value 9, the next has the value 7, the next 4 and the out side circle 1. 4 darts are thrown at the board (and always

Question 954869: A dart board has 4 concentric circles, the inner circle has the value 9, the next has the value 7, the next 4 and the out side circle 1. 4 darts are thrown at the board (and always hit!) how many different solutions are there when adding up the value of the 4 dart hits. e.g. if all darts hit the inner circle the answer would be 36 if they all hit the outer circle the answer would be 4. Some of the solutions will repeat e.g. 1+4+4+7=16 as would 4+4+4+4=16 therefore to me simply using 4! wouldn't work. This seems like it should be simple but I can't find an elegant way to solve it!
Many thanks, Michael

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
There are solutions or possible outcomes
For each position (4 of them) there are 4 possible choices so the total number of outcomes is

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