Calculate appearances of each of 5 variables in combinations of sums where 3 are chosen

Question

I know the selection of any 3 variables can be done in $\binom{5}{3} = 10$ ways. But how many times will each variable appear in the final sum?

Answer 1

If you think about it, there are $\binom{4}{3} = 4$ ways to form a sum without some particular variable, meaning that the variable in question occurs in $10-4=6$ sums.

Edit: Another alternative mode of reasoning goes as such:

We know there is no preference for a single variable over another, meaning all must occur an equal number of times. 10 sums with 3 variables each result in $30$ mentions of $5$ types of variables, meaning that each variable is represented $30/5=6$ times.