a dartboard has 3 rings worth 7 points, 4 points, and 1 point. if you throw three darts and they hit the board, how many different scores are possible? (each score is the sum of the three dart scores)

Question

a dartboard has 3 rings worth 7 points, 4 points, and 1 point. if you throw three darts and they hit the board, how many different scores are possible? (each score is the sum of the three dart scores)

Answer 1

If a dart hits the dartboard, the dart is either in a 7 point ring, a 4 point ring, or a 1 point ring.

That means each throw of the dart has three possible point outcomes.

1st Throw................2nd Throw................3rd Throw

1..............................1...............................1

4..............................4...............................4

7..............................7...............................7

The number of possible point scores for each throw is three.

SO, THERE ARE 3 x 3 x 3 = 27 POSSIBLE OUTCOMES,

BUT MANY ARE THE SAME SCORE.

THERE ARE 7 DIFFERENT SCORES.

111 = 3....................411 = 6....................711 = 9

114 = 6....................414 = 9...................714 = 12

117 = 9....................417 = 12.................717 = 15

141 = 6....................441 = 9..................741 = 12

144 = 9....................444 = 12................744 = 15

147 = 12..................447 = 15................747 = 18

177 = 15..................471 = 12................771 = 15

174 = 12..................474 = 15................774 = 18

177 = 15..................477 = 18................777 = 21

FROM THE 27 THROWS, THERE ARE 7 DIFFERENT SCORES: 3, 6, 9, 12, 15, 18, 21