I have three numbers $a,b$ and $c$
How many different additions can I have ?
$a + a + a = 3a$
$a + a + b = 2a + b$
However, $a + b + a =2a + b$ which is the same addition as above so I neglect it.
$b + b + b = 3b$
$a + b + c = a + b + c$
and so on , How many different sums can I have ? It's definitely not a permutation $3^3$ and not even a permutation with repetition and It is also definitely not $3!$
How many different additions and why ?