Target areas are worth 4, 2 and 1
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There are 27 ways three darts can hit targets because for each dart there are 3 possible targets: 3³=27.

We can produce a score for each of the 27 possibilities:

1+1+1=3, 1+1+2=4, 1+1+4=6,

1+2+1=4, 1+2+2=5, 1+2+4=7,

1+4+1=6, 1+4+2=7, 1+4+4=9,

2+1+1=4, 2+1+2=5, 2+1+4=7,

2+2+1=5, 2+2+2=6, 2+2+4=8,

2+4+1=7, 2+4+2=8, 2+4+4=10,

4+1+1=6, 4+1+2=7, 4+1+4=9,

4+2+1=7, 4+2+2=8, 4+2+4=10,

4+4+1=9, 4+4+2=10, 4+4+4=12.

So we can now write the nine different scores with their frequencies in brackets:

3(1), 4(3), 5(3), 6(4), 7(6), 8(3), 9(3), 10(3), 12(1).

For example, 7(6) means there are 6 ways of getting the score 7.

by Top Rated User (1.2m points)

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