Question

You throw three darts at the board shown. each dart hits the board and scores a 1​, 3​, or 9. how many different total scores can you​ make

Answer 1

Total number of Possible three digit number , using 1,3 and 9 ,either using all at once , or using 2 at a time , or using all three

=(First place can be arranged in 3 ways )×(Second place can be arranged in 3 ways )×(Third place can be arranged in 3 ways )

=3 × 3 ×3

=27 Numbers

We can make 27 different type of scores.

⇒All of them are(Sum of Total Score are=3,5,7,9,11,13,15,19,21,27)

1+1+1=3 3+3+3=9 9+9+9=27 1+3+9=13 1+9+3=13

1+1+9=11 1+1+3=5 9+3+3=15 3+1+9=13 3+9+1=13

1+9+1=11 1+3+1=5 3+9+3=15 9+3+1=13 9+1+3=13

9+1+1=11 3+1+1=5 3+3+9=15 9+9+1=19 1+9+9=19 3+9+9=21 9+9+3=21 9+1+9=19 3+1+3=7

9+3+9=21 1+3+3=7 3+3+1=7 ⇒ There are 10 Different Score in all.

Answer 2

In a game of darts which includes only three darts and three scores you can expect to make ten different total scores. Those total scores can be tabulated and listed as follows:
1+1+1=3
1+1+3=5
1+3+3=7
3+3+3=9
1+1+9=11
1+3+9=13
1+9+9=19
3+3+9=15
3+9+9=21
9+9+9=27