Someone shot 10 arrows at a target with 10 concentric rings, each being worth a different integer number of points from 1 to 10. How many different ways are there of scoring 10 points by doing this? (Note that not all the arrows have to hit the target and that order matters; 6 first then 4 is different from 4 first then 6. Also note that two or more arrows may hit the same ring.)
There is only one way of doing this with four arrows (1,2,3,4) and there are 10x9x8x7 ways of getting this: 5040.
With three arrows, there are four ways (1,2,7; 1,3,6; 1,4,5; 2,3,5) and 10x9x8 ways for each: 2160.
With two arrows, its again four ways (1,9; 2,8; 3,7; 4,6) and 10x9 ways each:360.
And with one arrow, it's only one way (10) and 10 ways of doing this.
So, the answer is 7561.
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