Three different members of the set {4,5,6,7,8,9} are chosen at random and added. How many different sums are possible?

10

Step-by-step explanation:

4+5+6=15,

4+5+7=16,

4+5+8=17,

4+5+9=18,

4+6+7=17,

4+6+8=18,

4+6+9=19,

4+7+8=19,

4+7+9=20,

4+8+9=21,

5+6+7=18,

5+6+8=19,

5+6+9=20,

5+7+8=20,

5+7+9=21,

5+8+9=22,

6+7+8=21,

6+7+9=22,

6+8+9=23,

7+8+9=24.

There are sums 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 10 different sums in total.

There are 10 sums that are possible