How many different sums of 2 numbers are possible from 5 numbers?

Answer 1

The first number can be any one of 5. For each of those . . .

The second number can be any one of the remaining 4.

So there are (5 x 4) = 20 ways to sum 2 numbers out of 5.

But the sum of (A+B) and the sum of (B+A) are really both the same thing,

although they both count among the 20 different ways.

In fact, if you look at the 20 different ways, you'll find that there are actually

only 10 different pairs of numbers, and each pair shows up on the list as both

(A+B) and (B+A).

So the answer to the question is: 10