#### Answer

10 ways

#### Work Step by Step

A dart can score a 1, 5 or a 10.
We are throwing 3 darts, and they all hit the board.
We won't differentiate between the darts, because for the total score, which dart hit which numbers doesn't matter.
Sorted from by the number of tens, fives, and ones hit, in that order, the different combinations are:
- We hit 3 tens for a score of $3*10=30$
- We hit 2 tens and a five for a score of $2*10+5=25$
- We hit 2 tens and a one for a score of $2*10+1=21$
- We hit a ten and two fives, for a score of $10+2*5=20$
- We hit a ten, a five and a one, for a score of $10+5+1=16$
- We hit a ten and 2 ones, for a score of $10+2*1=12$
- We hit 3 fives, for a score of $3*5=15$
- We hit 2 fives and a one, for a score of $2*5+1=11$
- We hit 1 five and 2 ones, for a score of $5+2*1=7$
- We hit 3 ones, for a score of $3*1=3$
This means that there are $10$ different total scores we can make.