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

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.