Question

Suppose that the three regions of a target like the one pictured are assigned point values of 3, 5, and 7. How many different point totals are possible if three darts are thrown and each lands somewhere on this target?

A. 15
B. 17
C. 18
D. 20

Answer 1

The number of different point totals possible when three darts are thrown at a target with regions valued at 3, 5, and 7 points is 15, by listing out all the unique combinations and calculating their respective point totals.

Step-by-step explanation:

The question asks us to find the number of different point totals possible if three darts are thrown at a target with regions valued at 3, 5, and 7 points. We will solve this problem by listing out all possible combinations of three darts hitting the target and then adding up the scores for each combination.

Possible scores for one dart are 3, 5, and 7. For three darts, these scores can be combined in different ways. We must consider also that scoring the same points several times is possible, so combinations like (3,3,3) or (5,5,5) are valid.

1. Combination (3,3,3) gives a total of 9 points.
2. Combination (3,3,5) gives a total of 11 points, and other permutations like (3,5,3) and (5,3,3) are also counted once because they result in the same total score.
3. Similar calculations are done for all possible combinations, without repetitions, leading to unique scores.

Listing all unique combinations, we realize that the different point totals possible are: 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and 24, which totals to 15 different scores. So the correct answer is A. 15.